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Without using calculator , find the value of $cos(105^{o})$
written 4.7 years ago by gravatar for teamques10 teamques10 ★ 65k modified 2.1 years ago by gravatar for pedsangini276 pedsangini276 • 4.8k
engineering mathematics
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written 4.7 years ago by gravatar for teamques10 teamques10 ★ 65k

Solution:

\begin{aligned} \cos \left(105^{\circ}\right) &=\cos \left(60^{\circ}+45^{\circ}\right) \ &=\cos 60^{\circ} \cos 45^{\circ}-\sin 60^{\circ} \sin 45^{\circ} \ &=\left(\frac{1}{2}\right)\left(\frac{1}{\sqrt{2}}\right)-\left(\frac{\sqrt{3}}{2}\right)\left(\frac{1}{\sqrt{2}}\right) \ &=\frac{1-\sqrt{3}}{2 \sqrt{2}} \quad \text { or } \quad-0.2588 \end{aligned}

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written 4.7 years ago by gravatar for teamques10 teamques10 ★ 65k

Solution:

\begin{aligned} \cos \left(105^{\circ}\right) &=\cos \left(60^{\circ}+45^{\circ}\right) \ &=\cos 60^{\circ} \cos 45^{\circ}-\sin 60^{\circ} \sin 45^{\circ} \ &=\left(\frac{1}{2}\right)\left(\frac{1}{\sqrt{2}}\right)-\left(\frac{\sqrt{3}}{2}\right)\left(\frac{1}{\sqrt{2}}\right) \ &=\frac{1-\sqrt{3}}{2 \sqrt{2}} \quad \text { or } \quad-0.2588 \end{aligned}

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