Question 464583: please help me verify using identities:
((sec theta - tan theta)^2 +1)/(sec theta csc theta -tan theta csc theta)=2tan theta Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! ((sec theta - tan theta)^2 +1)/(sec theta csc theta -tan theta csc theta)=2tan theta
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[(sec-tan)^2+1]/(sec*csc-tan*csc)=2tan
[sec^2-2sec*tan+tan^2+1]/[(1/cos)(1/sin)-(sin/cos)(1/sin)]
identity: tan^2+1=sec^2
[2sec^2-2(1/cos)(sin/cos)]/[1/(cos*sin)-sin/(cos*sin)]
(2/cos^2-2sin/cos^2)/(1-sin)/(cos*sin)
(2(1-sin)/cos^2)/(1-sin)/(cos*sin)
(1-sin) cancels out
2(cos*sin)/cos^2=2sin/cos=2tan
Identity verified: left side=right side
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