What are the steps to solve (sec∂-tan∂)²=(1-sin∂)/(1+sin∂)?

[chris99191]

1. First one is (sin2x+sinx)/(cos2x+cosx+1)=tanx
Second one is (sec∂-tan∂)²=(1-sin∂)/(1+sin∂)


2. Sec=1/cos tan=sin/cos cos²x+sin²x=1



3. 1. I think eventually the sinx/cosx need to cancel to make tanx and the 1 could be used to create a lot of options
2. I have tried to start with the left hand side. However i am unsure whether to expand the bracket or not. I've tried it with 1/cos but I couldn't get very far

 

[SammyS]

1. ...
Second one is (sec∂-tan∂)²=(1-sin∂)/(1+sin∂)

3. 1. I think eventually the sinx/cosx need to cancel to make tanx and the 1 could be used to create a lot of options
2. I have tried to start with the left hand side. However i am unsure whether to expand the bracket or not. I've tried it with 1/cos but I couldn't get very far

For 1. Second one:

Use sec(x) = 1/cos(x) and tan(x) = sin(x)/cos(x). They have a common denominator, so combine them into one fraction. After squaring, change cos²(∂) to 1 - sin²(∂) .