Verify the identity secx-secx sin^2x= cosx

Verify the identity secx-secx sin^2x= cosx

Question
Verify the identity \(\displaystyle{\sec{{x}}}-{\sec{{x}}}{{\sin}^{{2}}{x}}={\cos{{x}}}\)

Answers (1)

2021-02-12
\(\displaystyle{\sec{{x}}}-{\sec{{x}}}{{\sin}^{{2}}{x}}={\cos{{x}}}\)
\(\displaystyle{\sec{{x}}}{\left({1}-{{\sin}^{{2}}{x}}\right)}={\cos{{x}}}\)
because \(\displaystyle{{\sin}^{{x}}+}{{\cos}^{{x}}=}{1},{1}-{{\sin}^{{2}}{x}}={{\cos}^{{2}}{x}}\)
\(\displaystyle{\sec{{x}}}{{\cos}^{{2}}{x}}={\cos{{x}}}\)
\(\displaystyle{\left(\frac{{I}}{{\cos{{x}}}}\right)}{{\cos}^{{2}}{x}}={\cos{{x}}}\)
\(\displaystyle{\cos{{x}}}={\cos{{x}}}\)
0

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