If 0 < A, B < 45o , Cos(A + B) = 24/25 and Sin(A - B) = 15/17 , then tan2A is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e 416/87
| Understanding | Application |
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tan2A = tan{(A+B) + (A-B)} ⇒ tan2A = tan(A + B) + tan(A - B) / 1 - tan(A + B) × tan(A - B) |
We have given that cos(A + B) = 24 / 25 ⇒ sin(A + B) = 7 / 25 We have given that sin(A - B) = 15 / 17 ⇒ cos(A - B) = 8 / 17 By the formula tanθ = sinθ / cosθ ⇒ tan(A + B) = 7 / 24, tan(A - B) = 15 / 8 ⇒ tan2A = (7 / 24 + 15 / 8) / 1 - (7 / 24) × (15 / 8) ⇒ 416 / 87 |