Question

If cos theta = 3/5 find sin theta - cot theta / 2 tan theta

Answer 1

Answer:

$\frac{sin\theta-cot\theta}{2\:tan\theta}=\frac{3}{160}$

Step-by-step explanation:

Given:

$cos\theta=\frac{3}{5}$

$sin^2\theta=1-cos^2\theta$

$\implies\:sin^2\theta=1-(\frac{3}{5})^2$

$\implies\:sin^2\theta=1-\frac{9}{25}$

$\implies\:sin^2\theta=\frac{16}{25}$

$\implies\:\bf{sin\theta=\frac{4}{5}}$

$tan\theta=\frac{sin\theta}{cos\theta}$

$tan\theta=\frac{4/5}{3/5}$

$\implies\:\bf{tan\theta=\frac{4}{3}}$

$\implies\:\bf{cot\theta=\frac{3}{4}}$

Now,

$\frac{sin\theta-cot\theta}{2\:tan\theta}$

$=\frac{\frac{4}{5}-\frac{3}{4}}{2(\frac{4}{3})}$

$=\frac{\frac{16-15}{20}}{\frac{8}{3}}$

$=\frac{\frac{1}{20}}{\frac{8}{3}}$

$=\frac{1}{20}\times\frac{3}{8}$

$=\frac{3}{160}$

$\implies\boxed{\bf{\frac{sin\theta-cot\theta}{2\:tan\theta}=\frac{3}{160}}}$

Answer 2

Answer:

Step-by-step explanation:. Sorry for the bad handwriting