Please show all work. Thank you!

Please note thta:

cos[2(theta)]= (cos (theta))^2 - (sin(theta))^2 = 1 - 2* (sin(theta))^2

Next I substitute the above identity into your expression, as below:

left side = - [1 - 2 (sin(theta))^2]/[sin(theta)] =

= - 1/[sin(theta)] + 2 sin(theta) = 2 sin(theta) - 1/[sin(theta)] =

= 2 sin(theta) - cosec(theta) = right side

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