Nomor 3-4 yang identitas trigonometri Tolong jawab : Buktikan identitas Trigonometri 1. Tan² A / 1 + Sec A = Sec A -1 2. 1 - cot⁴A = 2.Cossec² A - Cossec⁴ A Mak

[tex]$\begin{align}\frac{\tan^2a}{1+\sec a}&=\frac{~\dfrac{\sin^2a}{\cos^2a}~}{~\dfrac{\cos a}{\cos a}+\dfrac1{\cos a}~}\\&=\frac{\cos a(\sin^2a)}{\cos^2a(\cos a+1)}\\&=\frac{\sin^2a}{\cos a(\cos a+1)}\\&=\frac1{\cos a}\times\frac{\sin^2a}{\cos a+1}\\&=\sec a\times\frac{1-\cos^2a}{1+\cos a}\\&=\sec a\times\frac{(1+\cos a)(1-\cos a)}{1+\cos a}\\&=\sec a(1-\cos a)\\&=\sec a-\sec a\cdot\cos a\\&=\sec a-\frac1{\cos a}\cdot\cos a\\&=\boxed{\sec a-1}\ \bold{(terbukti)}\end[/tex]



[tex]$\begin{align}1-\cot^4a&=1-\frac{\cos^4a}{\sin^4a}\\&=\frac{\sin^4a-\cos^4a}{\sin^4a}\\&=\frac{(\sin^2a-\cos^2a)(\sin^2a+\cos^2a)}{\sin^4a}\\&=\frac{(\sin^2a-\cos^2a)(1)}{\sin^4a}\\&=\frac{(\sin^2a-(1-\sin^2a))}{\sin^4a}\\&=\frac{2\sin^2a-1}{\sin^4a}\\&=\frac{2\sin^2a}{\sin^4a}-\frac1{\sin^4a}\\&=\frac2{\sin^2a}-\frac1{\sin^4a}\\&=\boxed{2\cdot\csc^2a-\csc^4a}\ \bold{(terbukti)}\end[/tex]