Answer to Question #217345 in Trigonometry for nonas

Question

Assume f(x) = sin(x+/π4)cos(π/4) + cos(x+/π4)sin(π/4) for all x elements of R. Which of the following statements is correct?

A. f(x) = -cos(x)

B. f(x) = sin(x)

C. f(x) = cos(x)

D. f(x) = -sin(x)

Answer 1

Solution:

$f(x) = \sin(x+\fracπ4)\cos(\fracπ4) + \cos(x+\fracπ4)\sin(\fracπ4)$

Using $\sin A \cos B +\cos A \sin B=\sin (A+B)$

$f(x) = \sin(x+\fracπ4+\fracπ4)=\sin(\fracπ2+x)=\cos x$

Hence, option (C) is correct.