Question

verify identity : 1/(tanB+cotB) = sinBcosB

Answer 1

\(\bf \cfrac{1}{tan(B)+cot(B)}=sin(B)cos(B)
\\ \quad \\ \quad \\
\cfrac{1}{tan(B)+cot(B)}\implies \cfrac{1}{\frac{sin(B)}{cos(B)}+\frac{cos(B)}{sin(B)}}
\\ \quad \\
\implies \cfrac{1}{\frac{[sin(B)sin(B)]+[cos(B)cos(B)]}{cos(B)sin(B)}}
\\ \quad \\
recall \implies {\color{blue}{ sin^2(\theta)+cos^2(\theta)=1\qquad \qquad \cfrac{\quad \frac{a}{b}\quad }{\frac{c}{d}}\implies \cfrac{a}{b}\cdot \cfrac{d}{c}}}\)