The real part of $\sin \log (x+i y)$ is

$\sin \left(\log \sqrt{x^2+y^2}\right) \sinh \left(\tan ^{-1} \frac{y}{x}\right)$

JEE MATHEMATICS MCQ: HYPERBOLIC FUNCTIONS

1 Easy

1 of 1

Application +4 | -1

The real part of

\sin \log (x+i y)

View answer and explanation

Correct option: C

\sin \left(\log \sqrt{x^2+y^2}\right) \cosh \left(\tan ^{-1} \frac{y}{x}\right)

Option C (

\sin (\log \sqrt{{x^2+y^2}}) \cosh (\tan ^{-1} \frac{{y}}{{x}})

) is correct because it correctly identifies the real part of the expression after applying trigonometric identities and logarithmic properties.