Prove that: (1+\frac{1}{\tan^2A})(1+\frac{1}{\cot^2A})=\frac{1}{\sin^2A

amanf 2021-08-22 Answered
Prove that:
(1+1tan2A)(1+1cot2A)=1sin2Asin4A
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Expert Answer

Clara Reese
Answered 2021-08-23 Author has 120 answers
We use the basic trigonometry formula to solve the equation.
Prove: (1+1tan2A)(1+1cot2A)=1sin2Asin4A
L.H.S.=(1+1tan2A)(1+1cot2A)
=(tan2A+1tan2A)(cot2A+1cot2A)
=(sec2Atan2A)(csc2Acot2A)
=(1cos2Asin2Acos2A)(1sin2Acos2Asin2A)
=(1sin2A)(1cos2A)
=(1sin2A)(11sin2A)
=1sin2Asin4A
L.H.S=R.H.S
Hence prove.
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