Find the value of sin(π+θ)sin(π-θ)cosec2θ.
1
-1
sinθ
-sinθ
Find the value of the given expression
Given expression: sin(π+θ)sin(π-θ)cosec2θ.
Since sin is a periodic function of time period 2π, also positive in second quadrant and negative in third quadrant or sin(π-θ)=sinθ,sin(π+θ)=−sinθ,whereπ=180∘
So,
sin(π+θ)sin(π-θ)cosec2θ=-sinθsinθcosec2θ=-sin2θ×1sin2θ[∵cosecθ=1sinθ]=-1
Hence, the value of sin(π+θ)sin(π-θ)cosec2θ is -1.