NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

If the range of f x = t a n - 1 x + 2 s i n - 1 x + c o s - 1 x is a , b , then

Options

Aa = π 4
Ba = - π 2
Cb = 5 π 4
Db = 3 π 2

Correct answer

C. b = 5 π 4

Step-by-step solution

f x = t a n - 1 x + s i n - 1 x + s i n - 1 x + c o s - 1 x f x = t a n - 1 x + s i n - 1 x + π 2 ; x ∈ - 1,1 ∵ s i n - 1 x + c o s - 1 x = π 2 ∵ f x is an increasing function ∴ Range of f x ∈ f - 1 , f 1 f - 1 = t a n - 1 - 1 + s i n - 1 - 1 + π 2 = - π 4 f 1 = t a n - 1 1 + s i n - 1 1 + π 2 = 5 π 4 ∴ Range of f x ∈ - π 4 , 5 π 4

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