Question

(1+cosx)/sinx=cscx+cotx

Trigonometric Functions
ANSWERED
asked 2021-06-22
\(\displaystyle\frac{{{1}+{\cos{{x}}}}}{{\sin{{x}}}}={\csc{{x}}}+{\cot{{x}}}\)

Answers (1)

2021-06-23

Work on the more complex side, which is the left side.
Separate as:
\(\displaystyle\frac{{{1}+{\cos{{x}}}}}{{\sin{{x}}}}={\left(\frac{{1}}{{\sin{{x}}}}\right)}+{\left(\frac{\cos x}{{\sin{{x}}}}\right)}\)
Use the reciprocal identity \(\displaystyle{\csc{{x}}}=\frac{{1}}{{\sin{{x}}}}\) and quotient identity \(\displaystyle{\cot{{x}}}=\frac{{\cos{{x}}}}{{\sin{{x}}}}\)
\(\displaystyle\frac{{{1}+{\cos{{x}}}}}{{\sin{{x}}}}={\csc{{x}}}+{\cot{{x}}}\)

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