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Answer 1 · 2017-11-30T18:50:11

Eeeezy peeeezy....

#cos^2theta/(1-sin theta) - 1 =#

#(1-sin^2theta)/(1-sin theta) - (1-sintheta)/(1-sintheta)#

# = (-sin^2theta + sintheta)/(1-sintheta)#

#= (sintheta(1-sintheta))/(1-sintheta)#

# = sintheta#

GOOD LUCK

Answer 2 · 2017-11-30T19:02:18

See below.

Not sure if you are asking to prove this, or you are looking to solve it as an equation for specific values of theta.

This is not an identity, so it can't be proved.

LHS

Let #theta=pi/2#

#(cos^2(pi/2))/(1-sin(pi/2))-1=0/(1-1)-1=#( division by zero)

RHS:

#sin(pi/2)=1#

#LHS!=RHS#