Question

prove that (1+cos)(1-cos) cosec^2=1​

Answer 1

LHS
By identity III in (1+cosθ)(1-cosθ)
=> 1-cos^2θ ..........(1)
And
Cosec^2θ= 1/ sin^2θ. .........(2)

Also we know that by trigonometric identity 1-cos^2θ= sin^2θ. ...........(3)

Νοώ putting up the values from 2&3
Sin^2 θ + 1/sin^2θ
=> sin^2θ/sin^2θ = 1
RHS=1

Hence proved

Hope this will help you:)