Question

Verify the identity cosx/1-sinx-tanx=1/cosx

Trigonometric equation and identitie
ANSWERED
asked 2021-01-28
Verify the identity \(\displaystyle\frac{{\cos{{x}}}}{{1}}-{\sin{{x}}}-{\tan{{x}}}=\frac{{1}}{{\cos{{x}}}}\)

Expert Answers (1)

2021-01-29
\(\displaystyle\frac{{\cos{{\left({x}\right)}}}}{{{1}-{\sin{{\left({x}\right)}}}}}-{\tan{{\left({x}\right)}}}=\)
\(\displaystyle\frac{{\cos{{\left({x}\right)}}}}{{{1}-{\sin{{\left({x}\right)}}}}}-\frac{{\sin{{\left({x}\right)}}}}{{\cos{{\left({x}\right)}}}}=\)
\(\displaystyle{\left({{\cos}^{{2}}{\left({x}\right)}}-{\sin{{\left({x}\right)}}}\frac{{{1}-{\sin{{\left({x}\right)}}}}}{{{\cos{{\left({x}\right)}}}{\left({1}-{\sin{{\left({x}\right)}}}\right)}}}=\right.}\)
\(\displaystyle\frac{{{{\cos}^{{2}}{\left({x}\right)}}-{\sin{{\left({x}\right)}}}+{{\sin}^{{2}}{\left({x}\right)}}}}{{{\cos{{\left({x}\right)}}}{\left({1}-{\sin{{\left({x}\right)}}}\right)}}}=\)
\(\displaystyle\frac{{{1}-{\sin{{\left({x}\right)}}}}}{{{\cos{{\left({x}\right)}}}{\left({1}-{\sin{{\left({x}\right)}}}\right)}}}=\)
\(\displaystyle\frac{{1}}{{\cos{{\left({x}\right)}}}}{Q}{E}{D}\)
6
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...