SOLUTION: (tan(theta)-cot(theta))/(tan(theta)+cot(theta))+2cos^2(theta)=1

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Question 522702: (tan(theta)-cot(theta))/(tan(theta)+cot(theta))+2cos^2(theta)=1
Answer by Aswathy(23) About Me  (Show Source):
You can put this solution on YOUR website!
Note that I have typed angle A instead of theta.
LHS= (tan A-cot A)/(tan A+cot A)+2cos^2 A
= [(sin A/cos A)-( cos A/sin A)] / [(sin A/cos A)+( cos A/sin A)] +2cos^2 A
= [(sin^2 A-cos^2 A)/(sin A*cos A)] /[( sin^2 A+cos^2 A)]/( sin A*cos A) +2cos^2 A
= (sin^2 A-cos^2 A)/1 +(2cos^2 A) [by using the identity sin^2 A+cos^2 A=1 and by canceling out the common term sin A*cos A]
= sin^2 A-cos^2 A+2cos^2 A
=sin^2 A+cos ^2 A
=1=RHS