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

RRB Junior Engineer Stage 1 Model Papers 3

Question : 16 of 100

Marks: +1, -0

The value of

\sin^2 2°+\sin^2 4°+\sin^2 6°+.....+\sin^2 90°

Solution:

\sin^2 2°+\sin^2 4°+\sin^2 6°+.....+\sin^2 86°+\sin^2 88°+\sin^2 90°

⇒\sin^2 2°+\sin^2 4°+\sin^2 6°+.....+\sin^2 (90°-4°)+\sin^2 (90°-2°)+\sin^2 90°

⇒\sin^2 2°+\sin^2 4°+\sin^2 6°+.....+\cos^2 4°+\cos^2 2°+\sin^2 90°

⇒(\sin^2 2°+\cos^2 2°)+(\sin^2 4°+\cos^2 4°)+(\sin^2 6°+\cos^2 6°)+\sin^2 90°

⇒(1+1+....22 \terms)+\sin^2 90°

⇒22+1=23

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