Exercise
$\frac{\left(sinx+cosx\right)\left(siny+cosy\right)}{sin\left(x+y\right)+cos\left(x-y\right)}$
Step-by-step Solution
Learn how to solve limits to infinity problems step by step online. Simplify the trigonometric expression ((sin(x)+cos(x))(sin(y)+cos(y)))/(sin(x+y)+cos(x-y)). 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 y. Using the sine of a sum formula: \sin(\alpha\pm\beta)=\sin(\alpha)\cos(\beta)\pm\cos(\alpha)\sin(\beta), where angle \alpha equals x, and angle \beta equals y. Factoring by \sin\left(x\right). Apply the addition formula: \sin\left(x+\frac{\pi}{4}\right)=\frac{\sin\left(x\right)}{\sqrt{2}}+\frac{\cos\left(x\right)}{\sqrt{2}}.
Simplify the trigonometric expression ((sin(x)+cos(x))(sin(y)+cos(y)))/(sin(x+y)+cos(x-y))
Final answer to the exercise
$\frac{\sin\left(y\right)+\cos\left(y\right)}{\sqrt{2}\sin\left(y+45\right)}$