Question

Prove that sinA- 2sin3 A/2cos3 A-cos A = tan A

Answer 1

$\dfrac{sin \: A \: - \: 2 {sin}^{3} A}{2 {cos}^{2} A \: - \: cos \: A} \: = \: tan \: A$

____________ [GIVEN]

• We have to prove L.H.S. = R.H.S.

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Take L.H.S.

=> $\dfrac{sin \: A \: - \: 2 {sin}^{3} A}{2 {cos}^{2} A \: - \: cos \: A}$

=> $\dfrac{sin \: A \: (1 \: - \: 2 {sin}^{2}A) }{cos \: A \: (2 {cos}^{2} A\: - \: 1)}$

• 1 - 2sin²A = cos2A

• 2cos²A - 1 = cos2A

=> $\dfrac{sin\:A}{cos\:A}$ × $\dfrac{cos2A}{cos2A}$

=> $\dfrac{sin\:A}{cos\:A}$

=> tan A

L.H.S = R.H.S.

______ [HENCE PROVED]

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