Question

To find the equation: \displaystyle\frac{{ \sin{{x}}+ \sin{{x}} \tan{{x}}}}{{{1}+ \tan{{x}}}}= \sin{{x}}

Trigonometric Functions
ANSWERED
asked 2021-05-14

To find the equation: \(\displaystyle\frac{{ \sin{{x}}+ \sin{{x}} \tan{{x}}}}{{{1}+ \tan{{x}}}}= \sin{{x}}\)

Answers (1)

2021-05-15

Work on the left side.

Factor oout sinx from the numerator:

\(\displaystyle\frac{{ \sin{{x}}+ \sin{{x}} \tan{{x}}}}{{{1}+ \tan{{x}}}}= \sin{{x}}=\frac{{ \sin{{x}}{\left({1}+ \tan{{x}}\right)}}}{{{1}+ \tan{{x}}}}\)

Cancel out

\(\displaystyle{1}+ \tan{{x}}\)

\(\displaystyle\frac{{ \sin{{x}}+ \sin{{x}} \tan{{x}}}}{{{1}+ \tan{{x}}}}= \sin{{x}}\)

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