**5.7.6 Fungsi Trigonometri, SPM Praktis (Kertas 1)**

**Soalan 15:**

Buktikan identiti $\frac{2}{kos2A+1}=se{k}^{2}A$

*Peneyelesaian:***Soalan 16:**

Buktikan identiti $\frac{2\mathrm{tan}A}{2-se{k}^{2}A}=\mathrm{tan}2A$

*Peneyelesaian:***Soalan 17:**

Buktikan identiti tan

*x*+ kot*x*= 2 kosek 2*x*

*Peneyelesaian:*Sebelah kiri,

tan

$\begin{array}{l}=\frac{\mathrm{sin}x}{kosx}+\frac{kosx}{\mathrm{sin}x}\\ =\frac{{\mathrm{sin}}^{2}x+ko{s}^{2}x}{kosx\mathrm{sin}x}\\ =\frac{1}{kosx\mathrm{sin}x}\leftarrow \overline{){\mathrm{sin}}^{2}x+ko{s}^{2}x=1}\\ =\frac{1}{\frac{1}{2}\mathrm{sin}2x}\leftarrow \overline{)\begin{array}{l}\mathrm{sin}2x=2\mathrm{sin}xkosx\\ \frac{1}{2}\mathrm{sin}2x=\mathrm{sin}xkosx\end{array}}\\ =\frac{2}{\mathrm{sin}2x}\\ =2\left(\frac{1}{\mathrm{sin}2x}\right)\\ =2kosek\text{}2x\\ =\text{Sebelahkanan}\end{array}$*x*+ kot*x***Soalan 18:**

Buktikan identiti $\frac{kosx-\mathrm{sin}2x}{kos2x+\mathrm{sin}x-1}=\frac{1}{\mathrm{tan}x}$

*Peneyelesaian:*