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1983

JEE Main 1983 Mathematics question on Inverse Trigonometric Functions

The value of tan⁡[cos⁡−1(45)+tan⁡−1(23)]\tan\left[\cos^{-1}\left(\frac{4}{5}\right) + \tan^{-1}\left(\frac{2}{3}\right)\right] is
  1. A.
    617\frac{6}{17}
  2. B.
    176\frac{17}{6}
  3. C.
    167\frac{16}{7}
  4. D.
    None of these
Show answer and solution

Correct option: B

Solution

Let α = cos⁻¹(4/5), so tan α = 3/4. Let β = tan⁻¹(2/3), so tan β = 2/3.

Using tan(α + β) = (tan α + tan β)/(1 − tan α · tan β):

Numerator: 3/4 + 2/3 = 9/12 + 8/12 = 17/12

Denominator: 1 − (3/4)(2/3) = 1 − 1/2 = 1/2

tan(α + β) = (17/12)/(1/2) = 17/6.

[1983]

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