Question #0e194

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Question #0e194

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Answer 1 · 2017-04-07T03:51:38

First, change all trigonometric functions to $sin(x)$ and $cos(x)$ by using the identities $csc(x)=1/sin(x)$ and $cot(x)=1/tan(x)=1/(sin(x)/cos(x))=cos(x)/sin(x)$ .

This results in $sin(x)/(1-cos(x))=1/sin(x)+cos/sin(x)$ . Add the two fractions on the right-hand side: $sin(x)/(1-cos(x))=(1+cos(x))/sin(x)$ .

Now, multiply both sides by $sin(x)(1-cos(x))$ to eliminate the fractions. The equation becomes $sin^2(x)=(1+cos(x))(1-cos(x))$ . Expand the right-hand side by using the identity $(a+b)(a-b)=a^2-b^2$ .

This results in $sin^2(x)=1-cos^2(x)$ . Add $cos^2(x)$ to both sides to get $sin^2(x)+cos^2(x)=1$ , which is one of the trigonometry identites.

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Question #0e194

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