Question

find the value of sin(π+x)sin(π-x)cosec square

Answer 1

We have, sin(π+x)sin(π-x)cosec^2.............(i)

We know
,sin(π+x)= -sinx.............(1)
and sin(π-x)= sinx............(2)

Substituting (1) and (2) in (i)
=> (-sinx)(sinx)cosec^2x
=> (-sin^2x)(cosec^2x).................(3)

We know,cosecx= 1/sinx
So,cosec^2x=1/sin^2x

Substituting in (3)
We get,
=>(-sin^2x)(1/sin^2x)= -1

So,the answer is -1.

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