Question

Verify the identity tan xx csc^2x - tan x = cot

Trigonometric equation and identitie
ANSWERED
asked 2021-09-06
Verify the identity
\(\displaystyle{\tan{\times}}{{\csc}^{{2}}{x}}–{\tan{{x}}}={\cot{}}\)

Expert Answers (1)

2021-09-07
\(\displaystyle{\tan{\times}}{{\csc}^{{2}}{x}}–{\tan{{x}}}=\)
\(\displaystyle={\tan{{x}}}\times\frac{{1}}{{{\sin}^{{2}}{x}}}–{\tan{{x}}}=\)
\(\displaystyle=\frac{{{\sin{{x}}}\times{1}}}{{{\cos{{x}}}\times{{\sin}^{{2}}{x}}}}–\frac{{\sin{{x}}}}{{\cos{{x}}}}=\)
\(\displaystyle=\frac{{1}}{{{\sin{{x}}}\times{\cos{{x}}}}}–\frac{{\sin{{x}}}}{{\cos{{x}}}}=\)
\(\displaystyle=\frac{{{1}–{{\sin}^{{2}}{x}}}}{{{\sin{{x}}}\times{\cos{{x}}}}}=\frac{{{{\cos}^{{2}}{x}}}}{{{\sin{{x}}}\times{\cos{{x}}}}}=\frac{{\cos{{x}}}}{{\sin{{x}}}}={\cot{{x}}}\)
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