The value of \sin ^{2} 2^\circ+\sin ^{2} 4^\circ+\sin ^{2} 6^\circ +....+ \sin ^{2} 90^\circ is

SSC CPO SI and ASI 2016 Paper

Question : 146 of 200

Marks: +1, -0

The value of

\sin ^{2} 2°+\sin ^{2} 4°+\sin ^{2} 6°

+....+ \sin ^{2} 90°

Solution:

(4)

\sin ^{2} 2°+\sin ^{2} 4°+\sin ^{2} 6°+...+\sin ^{2} 88°+\sin ^{2} 90°

= (\sin ^{2} 2°+\sin ^{2} 88°)+ (\sin ^{2} 4°+\sin ^{2} 86°)+...

+ (\sin ^{2} 44°+\sin ^{2} 46°)+\sin ^{2} 90°

= (\sin ^{2} 2°+\cos ^{2} 2°)+ (\sin ^{2} 4°+\cos ^{2} 4°)+...

+ (\sin ^{2} 44°+\cos ^{2} 44°)+\sin ^{2} 90°

=\{1+1+....+(22

times

) \}+1

=22+1=23

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