Question

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Evaluate sin(π + x) sin(π – x) cosec² x​

Answer 1

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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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Answer 2

Answer:-

= Sin(π+x) sin(π-x) cosec²x

= Sin(-x) sinx cosec²x. [ Sin (π+θ) = -sinθ ].

[ sin (π-θ) = sinθ ].

= -sinx.sinx.cosec²x

= -sin²x.cosec²x

= -sin²x × 1/sin²x. [ 1/sinθ = cosecθ ].

= -1.