If \sin\theta + cosec\theta = 2, then find the value ofsin400\theta + cosec400\theta.

SSC CPO SI and ASI Model Paper 7

Question : 141 of 200

Marks: +1, -0

sinθ + cosecθ = 2

, then find the value of

sin400θ + cosec400θ.

Solution:

(2)

sinθ+ cosecθ= 2

⇒sinθ+1/{sinθ}= 2

⇒sin^2θ+ 1 = 2sinθ

⇒ (sinθ-1)^2 = 0

⇒sinθ= 1 = sin90°⇒θ = 90°

∴sin^400θ+ cosec^400θ

= (sin90°)^400 + (cosec90°)^400 = 1 +1 = 2

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