99 Percentile Qs Bank for JEE MainMathematicsTrigonometric Ratios & Identities
Consider the function defined by f x = sin ⁡ x 1 + tan 2 ⁡ x + cos ⁡ x 1 + cot 2 ⁡ x for permissible values. Then which of the following is true?
Options
- Af x = sin ⁡ 2 x for all x
- Bf x = sin ⁡ x cos ⁡ x - cos ⁡ x sin ⁡ x for all x ∈ R
- Cf x = 0 for π 2 < x < π
- Df x = sin ⁡ x for all x
Correct answer
C. f x = 0 for π 2 < x < π
Step-by-step solution
(i), (ii) and (iv) are clearly false, since f x is not defined for k π 2 , on the contrary the two RHS included in choices (i), (ii) and (iv) are defined for all x. (iii) is true since f x = sin ⁡ x cos ⁡ x | + cos ⁡ x sin ⁡ x | f x = sin ⁡ x cos ⁡ x - cos ⁡ x sin ⁡ x = 0 for π 2 < x < π