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In a trigonometry function Prove that 1+sin2A+cos2A/1+sin2A-cos2A=cotA

In a trigonometry function Prove that 1+sin2A+cos2A/1+sin2A-cos2A=cotA

Grade:10

1 Answers

Arun
25763 Points
4 years ago
Dear Shubham
We use formula of cos 2A such that 1 is cancelled out.
Hence in Numerator we will use cos 2A = 2 cos²A -1
But in denominator cos 2A = 1 - sin²A
And sin2A = 2 sinA cosA in both (numerator & denominator)
Now coming to the question
(2 sinA cosA + 2 cos²A)/(2 sinA cosA + 2 sin²A)
Take common 2 cosA from numerator and 2 sinA from denominator
2 cosA(sinA + cosA)/ 2 sinA (sinA + cosA)
= Cos A/sinA
= CotA 
= RHS
 
Hence proved
 
Regards
Arun(askIITians forum expert)

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