# Simplify sum of angles expression (Trigonometry)

I'm stuck on this.I need to simplify this given expression $$\cot(\fracπ4+\theta)(\cos^2\theta-\sin^2\theta)$$ So far I simplified the first parentheses to $\frac{\cos\theta-\sin\theta}{\cos\theta\sin\theta}$ which I dont if this is correct but now I dont know how to multiply this by the second parenthesis

• Let us continue what you started, writing $c$ for $\cos\theta$ and $s$ for $\sin\theta$: you already know the expression is $$A=\frac{c-s}{c+s}(c^2-s^2)$$ hence $$A=\frac{c-s}{c+s}(c-s)(c+s)=(c-s)^2=c^2+s^2-2cs.$$ Now, $c^2+s^2=1$ and $2cs=\sin(2\theta)$ hence $$A=1-2\sin\theta\cos\theta=1-\sin(2\theta).$$
– Did
Commented Nov 29, 2015 at 17:09
• @SimpleArt Yes I am sure I "did that right". Would you be kind enough to explain what is "by far incorrect" here?
– Did
Commented Jan 5, 2016 at 0:28
• @Did Oh my bad. It wasn't very obvious with your $c's$ and $s's$. Commented Jan 5, 2016 at 0:47
• You ought to put it in as an answer, not as a comment (in my opinion). Commented Jan 5, 2016 at 0:47

$$\cos^2(x) - \sin^2(x) = \cos(2x)$$
and $$\cot\left(\frac{\pi}{4} - x \right) = \tan\left(\frac{\pi}{4} + x\right)$$