## Trigonometry (11th Edition) Clone

$$1-\frac{1}{\sec^2x}=\sin^2 x$$
$$A=1-\frac{1}{\sec^2x}$$ $$A=1-\Big(\frac{1}{\sec x}\Big)^2$$ From Reciprocal Identities: $$\sec x=\frac{1}{\cos x}$$ therefore, $$\cos x=\frac{1}{\sec x}$$ so, $$\cos^2x=\Big(\frac{1}{\sec x}\Big)^2$$ That makes $A$ into $$A=1-\cos^2 x$$ $$A=\sin^2x\hspace{1cm}\text{(Pythagorean Identity)}$$