Question

2sec^2x-2sec^2xsinx-sin^2x-cos^2x=1 prove

Answer 1

\[2\sec^2x-2\sec^2xsin^2x-\sin^2x-\cos^2x=1\]
\[2\sec^2x(1-\sin^2x)-\sin^2x-\cos^2x=1\]
\[2\sec^2x(\cos^2x)-\sin^2x-\cos^2x=1\]
\[2(\frac{1}{\cos^2x})(\cos^2x)-\sin^2x-\cos^2x=1\]
\[2-\sin^2x-\cos^2x=1\]
\[2-(\sin^2x+\cos^2x)=1\]
\[2-1=1\]