Prove that: 2cos3A−cosAsinA−2sin3A=tanA.

To prove:- 2cos3A−cosAsinA−2sin3A=tanAProof:-Taking L.H.S.-2cos3A−cosAsinA−2sin3A=cosA(2cos2A−1)sinA(1−2sin2A)=cosAcos2AsinAcos2A(∵cos2x=1−2sin2x=2cos2x−1)=cosAsinA=tanA= R.H.S.Hence proved.

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Prove that: { A-2^{3} A}{2^{3}A- A}= A.

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Prove that: $\frac{sin A - 2 sin ^{3} A}{2 cos ^{3} A - cos A} = tan A$ .

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Prove that:

\frac{sin A - 2 sin ^{3} A}{2 cos ^{3} A - cos A} = tan A

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Text solutionVerified

To prove:-

\frac{sin A - 2 sin ^{3} A}{2 cos ^{3} A - cos A} = tan A

Proof:-

Taking L.H.S.-

\frac{sin A - 2 sin ^{3} A}{2 cos ^{3} A - cos A}

= \frac{sin A ( 1 - 2 sin ^{2} A )}{cos A ( 2 cos ^{2} A - 1 )}

= \frac{sin A cos 2 A}{cos A cos 2 A} (∵ cos 2 x = 1 - 2 sin^{2} x = 2 cos^{2} x - 1)

= \frac{sin A}{cos A}

= tan A

=

R.H.S.

Hence proved.

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Question Text	Prove that: $\frac{sin A - 2 sin ^{3} A}{2 cos ^{3} A - cos A} = tan A$ .
Answer Type	Text solution:1
Upvotes	150

Prove that: 2cos3A−cosAsinA−2sin3A​=tanA.

Text solutionVerified

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Prove that: $\frac{sin A - 2 sin ^{3} A}{2 cos ^{3} A - cos A} = tan A$ .