8. Introduction to Trigonometry
medium

Evaluate:

$\sin 25^{\circ} \cos 65^{\circ}+\cos 25^{\circ} \sin 65^{\circ}$

A

$2$

B

$-1$

C

$0$

D

$1$

Solution

$\sin 25^{\circ} \cos 65^{\circ}+\cos 25^{\circ} \sin 65^{\circ}$

$=\left(\sin 25^{\circ}\right)\left\{\cos \left(90^{\circ}-25^{\circ}\right)\right\}+\cos 25^{\circ}\left\{\sin \left(90^{\circ}-25^{\circ}\right)\right\}$

$=\left(\sin 25^{\circ}\right)\left(\sin 25^{\circ}\right)+\left(\cos 25^{\circ}\right)\left(\cos 25^{\circ}\right)$

$=\sin ^{2} 25^{\circ}+\cos ^{2} 25^{\circ}$

$=1\left(A s \sin ^{2} A+\cos ^{2} A=1\right)$

Standard 10
Mathematics

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