Question

buktikan identitas trigonometri berikut

[tex]\frac{tan^{2} x}{sec^{2} x} = sin^{2}[/tex]

Answer 1

Jawab:

Terbukti

Penjelasan dengan langkah-langkah:

[tex]\begin{aligned}\frac{\tan^2 x}{\sec^2 x}&\:=\frac{\frac{\sin^2 x}{\cos^2 x}}{\frac{1}{\cos^2 x}}\\\:&=\frac{\sin^2 x}{\cos^2 x}~\frac{\cos^2 x}{1}\\\:&=\sin^2 x\end{aligned}[/tex]

Cara lain menggunakan identitas Pythagoras

[tex]\begin{aligned}\frac{\tan^2 x}{\sec^2 x}&\:=\frac{\sec^2 x-1}{\sec^2 x}\\\:&=\frac{\sec^2 x}{\sec^2 x}-\frac{1}{\sec^2 x}\\\:&=1-\cos^2 x\\\:&=\sin^2 x\end{aligned}[/tex]