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OpenStudy (anonymous):
2sec^2x-2sec^2xsinx-sin^2x-cos^2x=1 prove
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OpenStudy (lalaly):
\[2\sec^2x-2\sec^2xsin^2x-\sin^2x-\cos^2x=1\] \[2\sec^2x(1-\sin^2x)-\sin^2x-\cos^2x=1\] \[2\sec^2x(\cos^2x)-\sin^2x-\cos^2x=1\] \[2(\frac{1}{\cos^2x})(\cos^2x)-\sin^2x-\cos^2x=1\] \[2-\sin^2x-\cos^2x=1\] \[2-(\sin^2x+\cos^2x)=1\] \[2-1=1\]
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