If 4\sin^2\theta -1=0 and angle θ is less than 90°, the value of \cos^2\theta + \tan^2\theta is :

SSC CHSL Model Paper 17

Question : 65 of 100

Marks: +1, -0

4\sin^2θ -1=0

and angle θ is less than 90°, the value of

\cos^2θ + \tan^2θ

is :

Solution:

4\sin^2θ-1=0

⇒4\sin^2θ=1

⇒\sin\θ=1/2

( ∵\θ < 90°)

∴\sinθ=\sin30° ⇒θ=30°

∴\cos^2θ+\tan^2θ

= \cos^2 30°+\tan^2 30°

=(√3/2)^2+(1/√3)^2

=3/4+1/3=13/12

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