If f(x) = sin log x,then the value of f(xy) + | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given $f(x) = \sin \log x$.First,calculate $f(xy)$:$f(xy) = \sin \log(xy) = \sin(\log x + \log y)$.Next,calculate $f\left( \frac{x}{y} \right)$:$f

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(B) Given $f(x) = \sin \log x$.First,calculate $f(xy)$:$f(xy) = \sin \log(xy) = \sin(\log x + \log y)$.Next,calculate $f\left( \frac{x}{y} \right)$:$f\left( \frac{x}{y} \right) = \sin \log\left( \frac{x}{y} \right) = \sin(\log x - \log y)$.Using the trigonometric identity $\sin(A + B) + \sin(A - B) = 2 \sin A \cos B$,where $A = \log x$ and $B = \log y$:$f(xy) + f\left( \frac{x}{y} \right) = \sin(\log x + \log y) + \sin(\log x - \log y) = 2 \sin(\log x) \cos(\log y)$.Since $f(x) = \sin \log x$,we have:$f(xy) + f\left( \frac{x}{y} \right) = 2 f(x) \cos \log y$.Therefore,the expression becomes:$2 f(x) \cos \log y - 2 f(x) \cos \log y = 0$.

If $f(x) = \sin \log x$,then the value of $f(xy) + f\left( \frac{x}{y} \right) - 2f(x) \cos \log y$ is equal to

Similar Questions

If $S$ is a set of polynomials $P(x)$ of degree $\le 2$ such that $P(0) = 0$,$P(1) = 1$,and $P'(x) > 0$ for all $x \in (0, 1)$,then which of the following describes $S$?

Which of the following pairs of functions are identical?

The number of solutions of the equation $2^x = x^2$ is

If $f(x) = \log_{e}\left(\frac{1-x}{1+x}\right)$,$|x| < 1$,then $f\left(\frac{2x}{1+x^2}\right)$ is equal to

If $f(a) = \log \left| \frac{1-a}{1+a} \right|$ for $a \neq \{-1, 1\}$,then the set of values of all $a$,for which $f\left( \frac{2a}{1+a^2} \right) > 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module