SOLUTION: Please help me verify this identity and the steps if you can so I can understand 1 / 1 + sin of theta + 1 / 1

SOLUTION: Please help me verify this identity and the steps if you can so I can understand 1 / 1 + sin of theta + 1 / 1 - sin theta = 2 + 2 tan ^2 theta thanks!

Question 910695: Please help me verify this identity and the steps if you can so I can understand
1 / 1 + sin of theta + 1 / 1 - sin theta = 2 + 2 tan ^2 theta

thanks!
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
1 / 1 + sin of theta + 1 / 1 - sin theta
take the LCM
(1+sin theta +1 -sin Theta)/(1-sin^2 theta
= 2/(1-sin^2 theta)
=2/cos^2 theta
=2(sin^2theta+cos^2 theta)/cos^2 theta
= 2 sin^2 theta/cos^2 theta + 2 cos^2theta/cos^2 theta
2+ 2tan^2 theta

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