# The value of sin2 29° + sin2 61° is

Question:

The value of $\sin ^{2} 29^{\circ}+\sin ^{2} 61^{\circ}$ is

(a) 1

(b) 0

(c) $2 \sin ^{2} 29^{\circ}$

(d) $2 \cos ^{2} 61^{\circ}$

Solution:

The given expression is $\sin ^{2} 29^{\circ}+\sin ^{2} 61^{\circ}$.

$\sin ^{2} 29^{\circ}+\sin ^{2} 61^{\circ}$

$=\sin ^{2} 29^{\circ}+\left(\sin 61^{\circ}\right)^{2}$

$=\sin ^{2} 29^{\circ}+\left\{\sin \left(90^{\circ}-29^{\circ}\right)\right\}^{2}$

$=\sin ^{2} 29^{\circ}+\left(\cos 29^{\circ}\right)^{2}$

$=\sin ^{2} 29^{\circ}+\cos ^{2} 29^{\circ}$

$=1$

Hence, the correct option is (a).