If \tan^2\theta+\cot^2\theta=2, then what is the value of 2^{\sec\theta\cosec\theta}?

SSC CGL Model Paper 14

Question : 71 of 100

Marks: +1, -0

\tan^2θ+\cot^2θ=2,

then what is the value of

2^{\secθ\cosecθ}?

Solution:

\tan^2θ+\cot^2θ=2

⇒\tan^2θ+\cot^2θ-2=0

⇒\tan^2θ+\cot^2θ-2\tanθ\cotθ=0

⇒(\tanθ-\cotθ)^2=0

⇒\tanθ=\cotθ

⇒\tanθ=\tan(90°-θ)

⇒θ=90°-θ

⇒θ=45°

∴2^{\secθ\cosecθ}= 2^{\sec 45°\cosec45°}

=2^{ √2×√2}=2^2=4

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