Show all steps Using the pythagorean identities transform th

Show all steps.

Using the pythagorean identities, transform the following expression to obtain an expression involving only CSC Theta (1/cos Theta) + (1/cos Theta) =

Solution

(1_/cos)+(1_/cos)

=2_/cos

[we has sin²+cos²=1 =>cos=(1-sin²)]

=2_/(1-sin²)

[we have sin =1/csc]

=2_{/(1-(1/csc)²)}

=2_{/(1-(1/csc²))}

=2_{/((csc²-1)/csc²)}

=2csc² _/(csc²-1)

=2csc_/(csc²-1)

therefore

(1_/cos)+(1_/cos)=2csc_/(csc²-1)