Question

Prove that: 1+cosx/1-cosx=tan^2x/(secx-1)^2

Trigonometric equation and identitie
ANSWERED
asked 2021-02-23
Prove that: \(\displaystyle{1}+\frac{{\cos{{x}}}}{{1}}-{\cos{{x}}}=\frac{{{\tan}^{{2}}{x}}}{{\left({\sec{{x}}}-{1}\right)}^{{2}}}\)

Answers (1)

2021-02-24
\(\displaystyle\frac{{{1}+{\cos{{\left({x}\right)}}}}}{{{1}-{\cos{{\left({x}\right)}}}}}=\frac{{{1}-{{\cos}^{{2}}{\left({x}\right)}}}}{{\left({1}-{\cos{{\left({x}\right)}}}\right)}^{{2}}}=\)
\(\displaystyle\frac{{{\sin}^{{2}}{\left({x}\right)}}}{{{\cos}^{{2}}{\left({x}\right)}}}{\left({\sec{{\left({x}\right)}}}-{1}\right)}^{{2}}=\)
\(\displaystyle\frac{{{\tan}^{{2}}{\left({x}\right)}}}{{\left({\sec{{\left({x}\right)}}}-{1}\right)}^{{2}}}\)
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