Q41 of 354 Page 12

If (sin x)^y = (cos y)^x, prove that

Here,

Taking log on both sides,

[Using log =b log a]

Differentiating it with respect to x using product rule and chain rule,

Hence Proved.

If x^myⁿ = 1, prove that

If y^x = e^{y – x} prove that

If (cos x)^y = (tan y)^x, prove that

If e^x + e^y = e^{x + y}, prove that

If (sin x)y = (cos y)x, prove that