Question

Cos(-a)sina(1+ctg^2(-a))=ctga доказать тождество

Answer 1

Cos(-a)sin(a)(1+ctg^2(-a))=cos(a)*sin(a)(1+ctg^2(-a))=cos(a)sin(a)(1+(cos^2(-a)/(sin^2(-a))))=cos(a)sin(a)(1+cos^2(a)/sin^2(a))=cos(a)sin(a)(sin^2(a)+cos^2(a))/sin^2(a)=cos(a)sin(a)/sin^2(a)=cos(a)/sin(a)=ctg(a)

Answer 2

I can chat with you in Russian. You asked me to prove the identity $$\cos(-a)\sin a(1+\cot^2(-a))=\cot a$$ in detail. Here is one possible way to do it:

\begin{align*} \cos(-a)\sin a(1+\cot^2(-a)) &= \cos(-a)\sin a(1+\frac{\cos^2(-a)}{\sin^2(-a)}) \\ &= \cos(-a)\sin a\frac{\sin^2(-a)+\cos^2(-a)}{\sin^2(-a)} \\ &= \cos(-a)\sin a\frac{1}{\sin^2(-a)} \\ &= \frac{\cos(-a)}{\sin(-a)} \\ &= \cot(-a) \\ &= \cot a \end{align*}

I hope this helps. If you have any other questions, feel free to ask me.Ответь+подробно.+Cos(-a)sina(1+ctg^2(-a))=ctga+доказать+тождество