Establish the identity 1 sin theta cos theta1 sin theta

Establish the identity. 1 + sin theta + cos theta/1 + sin theta + cos theta = sin theta - cos theta/1 - cos theta Simplify the denominator of the fraction above by multiplying Do not, Use a trigonometric identity.. 3 (simplify your answer.) Apply a Pythagorean identity to the expression above M (Simplify your answer) Now that the denominator has been modified, thin row fraction can be seen to be equal to the loft side of the identity by which oi the following? Cancellation Property Pythagorean identity Even-Odd Identity

Solution

[sin/(1-cos)]

[sin/(1-cos)][(1+sin+cos)/(1+sin+cos)]

[sin(1+sin+cos)]/[(1-cos)(1+sin+cos)]

[sin(1+sin+cos)]/[1+sin+cos-cos-cossin-cos²]

simplified to [sin(1+sin+cos)]/[sin-cossin+1-cos²]

apply pythogorean identity: 1-cos²=sin²

[sin(1+sin+cos)]/[sin-cossin+sin²]

[sin(1+sin+cos)]/[sin(1-cos+sin)]

cancellation property

(1+sin+cos)]/(1-cos+sin)

(1+sin+cos)]/(1+sin-cos)