Question

convert 4√tan2A-sin2A to 4√tanAsinA
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Answer 1

Answer:

Given, sin 2A = 4/5

Therefore, 2tanA1+tan2A = 4/5

⇒ 4 + 4 tan2 A = 10 tan A

⇒ 4 tan2 A - 10 tan A + 4 = 0

⇒ 2 tan2 A - 5 tan A + 2 = 0

⇒ 2 tan2 A - 4 tan A - tan A + 2 = 0

⇒ 2 tan A (tan A - 2) - 1 (tan A - 2) =0

⇒ (tan A - 2) (2 tan A - 1) = 0

Therefore, tan A - 2 = 0 and 2 tan A - 1 = 0

⇒ tan A = 2 and tan A = 1/2

According to the problem, 0 ≤ A ≤ π/4

Therefore, tan A = 2 is impossible

Therefore, the required value of tan A is 1/2

Explanation:

sin 2A = 2 sin A cos A

⇒ sin 2A = 2 sinAcosA ∙ cos2 A

⇒ sin 2A = 2 tan A ∙ 1sec2A

⇒ sin 2A = 2tanA1+tan2A

There for sin 2A = 2tanA1+tan2A