How to simplify the expression (sinx+cosx)/(sinxcosx)?

kejuuoo

kejuuoo

Answered question

2022-12-27

How to simplify the expression sinx+cosxsinxcosx?

Answer & Explanation

Alana Walsh

Alana Walsh

Beginner2022-12-28Added 7 answers

\(\displaystyle\frac{{{\sin{{x}}}+{\cos{{x}}}}}{{{\sin{{x}}}{\cos{{x}}}}}\)
\(\displaystyle\Rightarrow\frac{{\sin{{x}}}}{{{\sin{{x}}}{\cos{{x}}}}}+\frac{{\cos{{x}}}}{{{\sin{{x}}}{\cos{{x}}}}}\)
\(\displaystyle\Rightarrow\frac{\cancel{{\sin{{x}}}}}{{\cancel{{\sin{{x}}}}{\cos{{x}}}}}+\frac{\cancel{{\cos{{x}}}}}{{{\sin{{x}}}\cancel{{\cos{{x}}}}}}\)
\(\displaystyle\Rightarrow\frac{{1}}{{\cos{{x}}}}+\frac{{1}}{{\sin{{x}}}}\)
\(\displaystyle\Rightarrow{\color{red}{{\sec{{x}}}+{\csc{{x}}}}}\)
bakouninetov

bakouninetov

Beginner2022-12-29Added 3 answers

sinx+cosxsinx.cosx=
=sinxsinx.cosx+cosxsinx.cosx==secx+cscx

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