Calculus 6

Calculus Level 5

If y = c o s − 1 cos ⁡ 3 x cos ⁡ 3 x \, y=cos^{-1}\sqrt{\dfrac{\cos{3x}}{\cos^3{x}}} \, then d y d x = a cos ⁡ b x + c o s d x \, \dfrac{dy}{dx}=\sqrt{\dfrac{a}{\cos{bx}+cos{dx}}} ,

where sin ⁡ x > 0 \sin{x}>0 . Find the value of a + b + d a+b+d .


The answer is 12.

Rudraksh Shukla by Rudraksh Shukla , 23, India

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1 solution

C Anshul
Jun 29, 2018

Just differentiate and simplify . You will get a=6 b and d are 2 & 4. In between you will see √((sin x)^2) which is |sin x|. That's why it is given sin x>0.

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