Exercise
$5cos\:\left(x\:+\frac{\pi}{4}\right)$
Step-by-step Solution
Learn how to solve multiply powers of same base problems step by step online. Simplify the trigonometric expression 5cos(x+pi/4). Using the cosine of a sum formula: \cos(\alpha\pm\beta)=\cos(\alpha)\cos(\beta)\mp\sin(\alpha)\sin(\beta), where angle \alpha equals x, and angle \beta equals \frac{\pi }{4}. The sine of \frac{\pi }{4} equals \frac{1}{\sqrt{2}}. The cosine of \frac{\pi }{4} equals \frac{1}{\sqrt{2}}. Multiplying the fraction by -1.
Simplify the trigonometric expression 5cos(x+pi/4)
Final answer to the exercise
$\frac{5\left(\cos\left(x\right)-\sin\left(x\right)\right)}{\sqrt{2}}$