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1
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9.5k
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1
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If $ y=sinpx + cospx$, prove that $ y_n \;=\; p^n [1+ (-1)^n sin2px ]$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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1
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1.3k
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Find $n^{th}$ derivative of $ 2^x \cdot cos^2\;x \cdot sin \; x $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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1
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1.6k
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Find $n^{th}$ order derivative of $y=cos\;x\;cos\;2x\;cos\;3x$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
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1.4k
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1
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Find $n^{th}$ order derivative of $\dfrac{x^2+4}{(x-1)^2(2x+3)}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
1
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1
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9.7k
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1
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If $ y=(sin^{-1}x)^2 \; $ obtain $ y_n(0)$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
1
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1
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1.4k
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1
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If $ y^{\dfrac{1}{m}} + y^{\dfrac{-1}{m}} \;=\; 2x $ prove that $ (x^2-1)y_{n+2} + (2n+1)xy_{n+1} + (n^2-m^2)y_n =0 $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
4
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1
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23k
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If $ y=cos(msin^{-1}x)$ , prove that $ (1-x^2)y_{n+2} -(2n+1)xy_{n+1} + (m^2-n^2)y_n=0 $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1.3k
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If $ y= \dfrac{sin^{-1}x}{\sqrt{1-x^2}} $ , Prove that $ (1-x^2)y_{n+2} -(2n+3) xy_{n+1} - (n^2+1) y_n = 0 $ Hence find $y_n(0)$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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1
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1.5k
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If $ y= \dfrac{sin^{-1}x}{\sqrt{1-x^2}} $ , Prove that $ (1-x^2)y_{n+1} -(2n+1) xy_{n} - n^2 y_{n-1} = 0 $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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If $ sin[log(x^2+2x+1)]$ ,prove that $(x+1)^2 y_{n+2}+(2n+1)(x+1) y_{n+1}+(n^2+4) y_n=0 $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
1
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1
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8.9k
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1
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Seperate into real and imaginary parts : $ tanh^{-1} (x+iy)$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
1
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1
answer
18k
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1
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Separate into real and imaginary parts of $ sin^{-1} e^{i\theta}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
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1.3k
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1
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Prove $tan \Bigg[ ilog \bigg ( \dfrac{a-ib}{a+ib} \bigg) \Bigg] \;=\; \dfrac{2ab}{a^2-b^2} $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
4
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1
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8.1k
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If $ cosec \bigg( \dfrac{\pi}{4} + ix \bigg) \;=\; u + iv $. Prove $ (u^2+v^2)^2 \;=\; 2(u^2-v^2) $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
1
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1
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4.9k
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If $cos(x+iy)cos(u+iv)=1 $ where x,y,u,v are real, then show that $ tan^2y \; cosh^2v \;=\; sin^2 u $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
4
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10k
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1
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Separate into real & imaginary parts: $ tan^{-1} (e^{i\theta}) $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
1
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1
answer
2.6k
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1
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If tan $ \bigg( \dfrac{\pi}{4} + iv \bigg) \;=\; re^{i\theta}$ Show : $ (i) r=1 \; (ii) \; tan \theta = sinh2v \; (iii) tanh v = tan \dfrac{\theta}{2} $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
9
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2
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21k
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2
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Complex Numbers : Solve $x^7+x^4+i(x^3+1)=0.$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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1
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1.5k
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1
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Solve the equation $x^6+1=0.$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
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1.1k
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($x+1 )^6 + (x-1)^6\;=\; 0 $ are given by $ -icot\Bigg[ \dfrac{(2k+1) \pi}{12} \Bigg] \; \; \;, K=0,1,2,3,5 $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
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5.5k
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1
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If $\tan (x+iy) = a+ib$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
2
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1
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4.6k
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1
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show that $\log[e^{i\alpha}+e^{i\beta}] =\log[2\cos(\dfrac {\alpha-\beta}2) + i(\dfrac {\alpha+\beta}2)]$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
2
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1
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7.0k
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1
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Show that $\tan^{-1}(\dfrac {x+iy}{x-iy})=\dfrac {\pi}4 +\dfrac i2 \log (\dfrac {x+y}{x-y})$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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3.2k
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If $\log\tan x=y$ then prove that $\sin h(n+1)y + \sin h(n-1)y=2\sin h\space\space ny\space \space cosec 2x $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
5
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1
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11k
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1
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Solve the equation $7\cos hx + 8\sin hx=1$ for real values of x
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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