Question

If 1- sin square A/cos square A = tan A find A

Answer 1

Answer:

If 1+ sin^2 A= 3sin A cos A, does tan A= 1?

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Vikas Gupta

Answered 3 years ago

1+sin2A=3sinAcosA

squaring both sides

1+2sin2A+sin4A=9sin2Acos2A

⟹1+2sin2A+sin4A=9sin2A(1−sin2A)

⟹1+2sin2A+sin4A=9sin2A−9sin4A

⟹10sin4A−7sin2A+1=0

⟹10sin2A−5sin2A−2sin2A+1=0

⟹5sin2A(2sin2A−1)−1(2sin2A−1)=0

⟹(5sin2A−1)(2sin2A−1)=0

∴sin2A=15 or sin2A=12

but ∵ we want to prove that tanA=1

∴ from sin2A=12

we get sinA=12–√

∴tanA=1