Prove the identity cos thetatan theta cot theta csctheta Fo

Prove the identity cos theta(tan theta + cot theta) =csctheta For each step in your solution, carefully document what you are doing. State the identity, formula, or property you are using.

Solution

cos(tan +cot)

=cos((sin/cos) +(cos/sin)) ...............step 1)write tan as sin/cos ,cot as cos/sin

=cos((sin² +cos²)/cossin))...............step 2) make compound fraction

=cos(1/cossin)).....................................step3)sin² +cos² =1 is the identity

=(cos/cossin)).......................................step 4) cancel out cos

=1/sin

=csc.........................................................step 5)rewrite 1/sin as csc

so cos(tan +cot)=csc