If sinθ + cosecθ = 2, then the value of \sin^7\theta+ \cosec^7 \theta is

SSC CHSL Model Paper 18

Question : 67 of 100

Marks: +1, -0

If sinθ + cosecθ = 2, then the value of

\sin^7θ+ \cosec^7 θ

Solution:

\sinθ + \cosecθ = 2

\Sinθ +1/{\sinθ }=2

\sin^2θ + 1 = 2 \sinθ

(\sin^2θ- 2\sinθ + 1) = 0

(\sinθ-1 ) ^2 = 0

\Sinθ =1 = \sin 90 °

θ= 9 0 °

so,

\sin^ 7θ +\cosec^7θ = 1 + 1 = 2

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