JEE Main202226 Jul 2022Morning ShiftMathematicsInverse Trigonometric FunctionsActual

tan 2 tan - 1 1 5 + sec - 1 5 2 + 2 tan - 1 1 8 is equal to:

Options

A1
B2
C1 4
D5 4

Correct answer

B. 2

Step-by-step solution

Given, tan 2 tan - 1 1 5 + sec - 1 5 2 + 2 tan - 1 1 8 = tan 2 tan - 1 1 5 + tan - 1 1 8 + tan - 1 1 2 = tan 2 tan - 1 1 5 + 1 8 1 - 1 40 + tan - 1 1 2 = tan 2 tan - 1 1 3 + tan - 1 1 2 = tan tan - 1 2 × 1 3 1 - 1 3 2 + tan - 1 1 2 = tan tan - 1 3 4 + tan - 1 1 2 = tan tan - 1 3 4 + 1 2 1 - 3 8 = tantan - 1 5 4 5 8 = tantan - 1 2 = 2

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