99 Percentile Qs Bank for JEE MainMathematicsInverse Trigonometric Functions

If x= cosec ( ⁻¹ ( ( ⁻¹ ( ( ⁻¹ a ) ) ) ) ) , a [0,1]

Options

Ax^2- a ^2=3
Bx^2+ a ^2=3
Cx^2- a ^2=2
Dx^2+ a ^2=2

Correct answer

B. x^2+ a ^2=3

Step-by-step solution

aligned & x= cosec ( ⁻¹ ( ( ⁻¹ ( ( ⁻¹ a ) ) ) ) ) & = cosec ( ⁻¹ ( ( ⁻¹ ( ( ⁻¹ 1 1- a ^2 ) ) ) ) ) & = cosec ( ⁻¹ ( ( ⁻¹ ( 1 1- a ^2 ) ) ) ) & = cosec ( ⁻¹ ( ( ⁻¹ 1 2- a ^2 ) ) ) & = cosec ( ⁻¹ ( 1 2- a ^2 ) ) & = cosec ( cosec ⁻¹ ( 3- a ^2 ) ) & x= 3- a ^2 & x^2+ a ^2=3 aligned

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