## Trigonometry (11th Edition) Clone

$$\cot^2\theta(1+\tan^2\theta)=\csc^2\theta$$
$$A=\cot^2\theta(1+\tan^2\theta)$$ - Pythagorean Identity: $$\tan^2\theta+1=\sec^2\theta$$ Replace into $A$: $$A=\cot^2\theta\times\sec^2\theta$$ - Quotient Identity: $$\cot\theta=\frac{\cos\theta}{\sin\theta}$$ - Reciprocal Identity: $$\sec\theta=\frac{1}{\cos\theta}$$ Replace them into $A$: $$A=\frac{\cos^2\theta}{\sin^2\theta}\times\frac{1}{\cos^2\theta}$$ $$A=\frac{1}{\sin^2\theta}=\Big(\frac{1}{\sin\theta}\Big)^2$$ $$A=\csc^2\theta\hspace{1cm}\text{(Reciprocal Identity)}$$