SSC CPO SI and ASI Model Paper 6

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Question : 140 of 200

Marks: +1, -0

If

sinθ + cosecθ = 2,

then find the value of

(sin^100 θ + cosec^100 θ).

0
1
2
– 1

Solution:

(3)

sinθ+ cosecθ = 2

⇒ sinθ+ 1/{sin}= 2

⇒ sin^2θ+ 1 = 2sinθ

⇒(sinθ-1)^2 = 0

⇒sinθ= 1

⇒θ = 90

°

∴ sin^100θ+ cosec^100θ

= (sin 90°)^100 + (cosec 90°)^100

= 1 + 1 = 2

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