Question

Evaluate : sin2 50°+sin2 40°

Answer 1

sin 2 50 + sin 2 40
=
2 sin 50 cos 50 + 2 sin 40 cos 40
=
2 (sin 50 cos 50 + sin 40 cos 40 )

Answer 2

$\fontsize{18}{10}{\textup{\textbf{The required value of the given expression is 1.}}}$

Step-by-step explanation:  The  given expression to evaluate is

$E=\sin^250^\circ+\sin^240^\circ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following two trigonometric formulas :

$(i)~\sin40^\circ=\cos(90^\circ-40^\circ),\\\\(ii)~\sin^2\theta+\cos^2\theta=1.$

Therefore, the value of expression (i) can be evaluated as follows :

$E\\\\=\sin^250^\circ+\sin^240^\circ\\\\=\sin^250^\circ+(\cos(90^\circ-40^\circ))^2\\\\=\sin^250^\circ+(\cos50^\circ)^2\\\\=\sin^250^\circ+\cos^250^\circ\\\\=1.$

Thus, the required value of the given expression is 1.

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