Question

If
value
of
sinx+ cosecx= 2 then value of
sin^10x+ cosec^10x
is equal to ?

Answer 1

$\huge\underline\red{Solution:-}$

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sinx+cosecx=2

⇒sinx+$\bf\frac{1}{sin\:x} =2$

⇒$\bf\sin^{2}$x+1=2sin x

⇒$\bf\sin^{2}$x-2 sin x+1=0

⇒$\bf(sin\:x-1) ^{2}$= 0

$\bf\⇒sinx=1 \\cosecx=1$

$\bf\sin^{10}\:x \:+ cosec^{2} \:x= 2$