MCQ
$\sin ^2 65^{\circ}+\sin ^2 25^{\circ}=$ ?
- A$0$
- ✓$1$
- C$\frac{3}{4}$
- DNone of these
✓
Answer
Correct option: B.
$1$
$\sin ^2 65^{\circ}+\sin ^2 25^{\circ} .$
$=\left[\sin \left(90^{\circ}-25^{\circ}\right)\right]^2+\sin ^2 25^{\circ} .$
$=\left(\cos 25^{\circ}\right)^2+\sin ^2 25^{\circ} .$
$=\cos ^2 25^{\circ}+\sin ^2 25^{\circ}$
$=1$
$=\left[\sin \left(90^{\circ}-25^{\circ}\right)\right]^2+\sin ^2 25^{\circ} .$
$=\left(\cos 25^{\circ}\right)^2+\sin ^2 25^{\circ} .$
$=\cos ^2 25^{\circ}+\sin ^2 25^{\circ}$
$=1$
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