Verify the following trigonometric identity cos theta1 sin

Verify the following trigonometric identity: cos theta/1 - sin theta = sec theta + tan theta Prove that

Solution

9)

cos_/(1-sin)

multiply numerator and denominator by 1+sin

=[cos(1+sin)]_{/[(1-sin)(1+sin)]}

=[cos(1+sin)]_/(1-sin²)

=[cos(1+sin)]_/(cos²)............................................since sin²+cos²=1 is an identity

=(1+sin)_/cos

=(1_/cos)+(sin_/cos)

=sec+tan