Write the expression in terms of sines and cosines and simpl

Write the expression in terms of sines and cosines and simplify so the answer is NOT a quotient. Select the expression that completes the identity sec alpha - cos alpha = cos^2 alpha sin alpha middot tan alpha cot^2 alpha middot cos^2 alpha 1 - cos^2 alpha 1 sin^2 alpha

Solution

sec -cos

write sec as 1/cos

=(1/cos) -cos

=(1-cos²)/cos

[since sin²+cos²=1 is identity =>1-cos²=sin²]

=[sin²]/[cos]

=(sinsin)/cos

=sin(sin/cos)

=sin.tan