99 Percentile Qs Bank for JEE MainMathematicsDifferentiation

If y = t a n - 1 s e c x - t a n x , then the absolute value of 2 d y d x is

Correct answer

Step-by-step solution

y = t a n - 1 s e c x - t a n x y = t a n - 1 1 - s i n x c o s x ⇒ y = t a n - 1 c o s x 2 - s i n x 2 2 c o s 2 x 2 - s i n 2 x 2 ⇒ y = t a n - 1 c o s x 2 - s i n x 2 c o s x 2 + s i n x 2 ⇒ y = t a n - 1 1 - t a n x 2 1 + t a n x 2 ⇒ y = t a n - 1 t a n π 4 - x 2 ⇒ y = π 4 - x 2 Differentiating with respect to x , we get ⇒ d y d x = - 1 2 = - 0.5

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