If sin θ+ cosec θ= 2, then find the value of \sin^400 \theta+ cosec^400 \theta.

RRB NTPC Prelims Model Paper 4 with solutions

Question : 41 of 100

Marks: +1, -0

If sin θ+ cosec θ= 2, then find the value of

sin^400 θ+ cosec^400 θ.

Solution:

(2) sinθ+ cosecθ= 2

⇒sinθ+ 1/sinθ= 2

⇒sin^2θ+ 1 = 2sinθ

⇒(sinθ-1)^2 = 0

⇒sinθ= 1 = sin90θ

⇒θ= 90°

⇒sin^400θ+ cosec^400 θ

= (sin90°)400 + (cosec 90°)400 = 1 +1 = 2

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