Bab 16 Fungsi Trigonometri

$\begin{array}{l}\text{Sebelah kiri}\\ \text{= }\frac{2}{kos2A+1}\\ =\frac{2}{\left(2ko{s}^{2}A-1\right)+1}\leftarrow \boxed{kos2A=2ko{s}^{2}A-1}\\ =\frac{2}{2ko{s}^{2}A}=\frac{1}{ko{s}^{2}A}\\ =se{k}^{2}A\\ =\text{Sebelah kanan}\end{array}$

$\begin{array}{l}\text{Sebelah kiri}\\ \text{= }\frac{2\tan A}{2-se{c}^{2}A}\\ =\frac{2\tan A}{2-\left({\tan }^{2}A+1\right)}\leftarrow \boxed{{\tan }^{2}A+1=se{c}^{2}A}\\ =\frac{2\tan A}{1-{\tan }^{2}A}\\ =\tan 2A\\ =\text{Sebelah kanan}\end{array}$

$\begin{array}{l}=\frac{\sin x}{kosx}+\frac{kosx}{\sin x}\\ =\frac{{\sin }^{2}x+ko{s}^{2}x}{kosx\sin x}\\ =\frac{1}{kosx\sin x}\leftarrow \boxed{{\sin }^{2}x+ko{s}^{2}x=1}\\ =\frac{1}{\frac{1}{2}\sin 2x}\leftarrow \boxed{\begin{array}{l}\sin 2x=2\sin xkosx\\ \frac{1}{2}\sin 2x=\sin xkosx\end{array}}\\ =\frac{2}{\sin 2x}\\ =2\left(\frac{1}{\sin 2x}\right)\\ =2kosek2x\\ =\text{Sebelah kanan}\end{array}$

$\begin{array}{l}\text{Sebelah kiri}\\ \frac{kosx-\sin 2x}{kos2x+\sin x-1}\\ =\frac{kosx-2\sin xkosx}{\left(1-2{\sin }^{2}x\right)+\sin x-1}\leftarrow \boxed{kos2x=1-2{\sin }^{2}x}\\ =\frac{kosx\left(1-2\sin x\right)}{\sin x-2{\sin }^{2}x}\\ =\frac{kosx\left(1-2\sin x\right)}{\sin x\left(1-2\sin x\right)}\\ =\frac{kosx}{\sin x}\\ =kotx\\ =\frac{1}{\tan x}\\ \text{Sebelah kanan}\end{array}$