What can you do to the equation sin^2(θ)+2θ+cos^2(θ)=1 to get the identity 1+cot^2(θ)=csc 2^(θ)?

Question

There may be more than one correct answer. Select all that apply.

Rewrite sin^2(θ)/cos^2(θ) using the tangent identity.
Simplify cos^2(θ)/cos^2(θ) to get 1.
Rewrite 1/cos^2(θ) using the reciprocal identity for secant.
Simplify sin^2(θ)sin^2(θ) to get 1.
Divide both sides of the equation by cos^2(θ).
Rewrite 1/sin^2(θ) using the reciprocal identity for cosecant.
Divide both sides of the equation by sin^2(θ).
Rewrite cos^2(θ)/sin^2(θ) using the cotangent identity.

Answer 1

If sin^2(θ)+2θ+cos^2(θ)=1 means:

sin² ( θ ) + cos² ( θ ) = 1

then

sin² ( θ ) + cos² ( θ ) = 1

Divide both sides by sin² ( θ )

sin² ( θ ) / sin² ( θ ) + cos² ( θ ) / sin² ( θ ) = 1 / sin² ( θ )

1 + [ cos ( θ ) / sin ( θ ) ]² = [ 1 / sin ( θ ) ]²

1 + cot² ( θ ) = csc² ( θ )

Answer 2

where did that 1 come from in step 3?

Answer 3

nevermind, that is sin^2(θ )/sin^2(θ ), Thank you!!!!