Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

If in a ∆ABC, a = 5, b = 4, A = π/2 + B, then C

1) is tan-1 (1/2)

2) is tan-1 (9/40)

3) cannot be evaluated

4) is tan-1 (1/9)

Solution:

Given a = 5, b = 4, A = π/2 + B

We know tan ((A – B)/2) = ((a – b)/(a + b)) cot (C/2)

So tan (π/4) = ((5 – 4)/(5 + 4))cot (C/2)

1 = (1/9) cot (C/2)

tan (C/2) = 1/9

We know tan C = 2 tan (C/2)/(1 – tan2(C/2)

= (2/9)/(1 – 1/81)

= (2/9)/(80/81)

= 9/40

So C = tan-1(9/40)

Hence option (2) is the answer.

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