SSC CGL 12 Aug 2017 Shift 1 Paper

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Question : 71 of 100

Marks: +1, -0

If

\sin 3 \θ \sec 2 \θ=1,

then what is the value of

[3 \tan ^{2}({5 \θ} / 2)-1\ ] ?

0
1
2
3

Solution:

\sin 3 \θ. \sec 2 \θ=1

⇒

\sin 3 \θ×{1}/{\cos 2 \θ }=1

⇒

\sin 3 \θ=\cos 2 \θ

⇒

\sin 3 \θ=\sin (90°-2 \θ )

⇒

3 \θ=90°-2 \θ

⇒

5 \θ=90°

∴

\θ= {90°}/{5}=18°

∴

[3 \tan ^{2}({5 \θ} / 2)-1\ ]

=3 \tan ^{2}({90° } / 2)-1

=

3 \tan ^{2}(45°)-1=3-1=2

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