SOLUTION: please help me verify using identities: ((sec theta - tan theta)^2 +1)/(sec theta csc theta -tan theta csc theta)=2tan theta

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
...
[(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
RELATED QUESTIONS
Please help me prove these following identities with explanation, thanks <3 1.) {{{... (answered by Alan3354)

The Cos(theta)= -0.5. Using trig identities determine the following values: 1)... (answered by richwmiller)

establish the identity: sec theta / csc theta + sin theta / cos theta = 2 tan... (answered by stanbon)

How do you verify the identity? Sec(theta)/csc(theta) +sin(theta)/cos(theta)=2... (answered by lwsshak3)

Verify that sec theta csc theta - tan theta = cot theta is an identity (answered by Alan3354)

sec square theta=2+2tan theta find tan... (answered by Timnewman)

-1/(csc(-theta)) - (cot(-theta))/(sec(-theta)) =... (answered by MathLover1,greenestamps)

How to solve the following: sin theta cot^2 theta sec ^2 theta = ? Answers: a)sec... (answered by lwsshak3)

what is the solution in proving the trigonometric identities: 1+cot theta/csc theta =... (answered by lwsshak3)