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Question: Solution of the equation \(\frac{dy}{dx} + \frac{1 + \cos 2y}{1 - \cos 2x}\) = 0 is...

Solution of the equation dydx+1+cos⁡2y1−cos⁡2x\frac{dy}{dx} + \frac{1 + \cos 2y}{1 - \cos 2x} = 0 is

A

tan y + cot x = c

B

tan y – cot x = c

C

cot x + tan y = c

D

None of these

Answer

tan y – cot x = c

Explanation

Solution

∫dy1+cos⁡2y=−∫dx1−cos⁡2x\int_{}^{}{\frac{dy}{1 + \cos 2y} = - \int_{}^{}\frac{dx}{1 - \cos 2x}}

Ž ∫12sec⁡2ydy=−12∫cos⁡ec2xdx\int_{}^{}{\frac{1}{2}\sec^{2}ydy = - \frac{1}{2}\int_{}^{}{\cos ec^{2}xdx}}

Ž 12tan⁡y=−12(−cot⁡x)+C\frac{1}{2}\tan y = - \frac{1}{2}( - \cot x) + CŽ tan y = cot + C