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Ilya [14]
3 years ago
5

Make tan(x)(csc(x)-sin(x)) into 1 trigononometrical value

Mathematics
1 answer:
o-na [289]3 years ago
7 0
\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\qquad\qquad  csc(\theta)=\cfrac{1}{sin(\theta)}
\\\\\\
sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\
-------------------------------\\\\
tan(x)[cos(x)-sin(x)]\implies \cfrac{sin(x)}{cos(x)}\left[ \cfrac{1}{sin(x)}-sin(x) \right]
\\\\\\
\cfrac{sin(x)}{cos(x)}\left[ \cfrac{1-sin^2(x)}{sin(x)}\right]\implies \cfrac{sin(x)}{cos(x)}\left[ \cfrac{cos^2(x)}{sin(x)}\right]\implies cos(x)
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