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Given tan theta/1-cot theta + cot theta/1-tan theta can be written as.
= sin theta/cos theta/(1-cos theta/sin theta) + cos theta/sin theta/(1-sin theta/cos theta)
= (sin^2 theta)/cos theta(sin theta - cos theta) + cos^2 theta/sin theta(cos theta - sin theta)
= sin^3 theta - cos^3 theta/sin theta cos theta(sin theta - cos theta)
= (sin theta - cos theta)(sin^2 theta + cos^2 theta + sin theta cos theta)/(sin theta cos theta(sin theta - cos theta)
= 1 + sin theta cos theta/sin theta cos theta
= 1 + sec theta cosec theta
LHS = RHS.
Hope this helps!
= sin theta/cos theta/(1-cos theta/sin theta) + cos theta/sin theta/(1-sin theta/cos theta)
= (sin^2 theta)/cos theta(sin theta - cos theta) + cos^2 theta/sin theta(cos theta - sin theta)
= sin^3 theta - cos^3 theta/sin theta cos theta(sin theta - cos theta)
= (sin theta - cos theta)(sin^2 theta + cos^2 theta + sin theta cos theta)/(sin theta cos theta(sin theta - cos theta)
= 1 + sin theta cos theta/sin theta cos theta
= 1 + sec theta cosec theta
LHS = RHS.
Hope this helps!
Rahi39:
Thank you so much :)
Helped me a lot
:)
Thank you so much rahi for the brainliest
Your welcome
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