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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