What is $\frac{3 cot θ}{5}$ $(3cottheta)/5$ in terms of $sec θ$ $sectheta$ ?

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What is $\frac{3 cot θ}{5}$ $(3cottheta)/5$ in terms of $sec θ$ $sectheta$ ?

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Answer 1 · 2016-04-15T01:27:04

$\frac{3}{5} \cdot cot θ = \frac{3}{5} \cdot \frac{\sqrt{{sec}^{2} θ - 1}}{{sec}^{2} θ - 1}$ $3/5*cot theta=3/5*sqrt(sec^2 theta-1)/(sec^2 theta-1)$

Explanation:

the given expression is

$\frac{3}{5} \cdot cot θ$ $3/5*cot theta$

${tan}^{2} θ + 1 = {sec}^{2} θ$ $tan^2 theta+1=sec^2 theta$

${tan}^{2} θ = {sec}^{2} θ - 1$ $tan^2 theta=sec^2 theta-1$

${cot}^{2} θ = \frac{1}{{tan}^{2} θ}$ $cot^2 theta=1/tan^2 theta$

${cot}^{2} θ = \frac{1}{{sec}^{2} θ - 1}$ $cot^2 theta=1/(sec^2 theta-1)$

$cot θ = \sqrt{\frac{1}{{sec}^{2} θ - 1}} = \frac{1}{\sqrt{{sec}^{2} θ - 1}} = \frac{\sqrt{{sec}^{2} θ - 1}}{{sec}^{2} θ - 1}$ $cot theta=sqrt(1/(sec^2 theta-1))=1/sqrt(sec^2 theta-1)=sqrt(sec^2 theta-1)/(sec^2 theta-1)$

Therefore

$\frac{3}{5} \cdot cot θ = \frac{3}{5} \cdot \frac{\sqrt{{sec}^{2} θ - 1}}{{sec}^{2} θ - 1}$ $3/5*cot theta=3/5*sqrt(sec^2 theta-1)/(sec^2 theta-1)$

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What is $\frac{3 cot θ}{5}$ $(3cottheta)/5$ in terms of $sec θ$ $sectheta$ ?

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