How do you find the value of $cot 2 θ$ $cot2theta$ given $cot θ = \frac{4}{3}$ $cottheta=4/3$ and $π < θ < \frac{3 π}{2}$ $pi<theta<(3pi)/2$ ?

Question

4346 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-21T06:07:34

$cot 2 θ = \frac{7}{24}$ $cot2theta=7/24$

$cot 2 θ = \frac{{cot}^{2} θ - 1}{2 cot θ}$ $cot2theta=(cot^2theta-1)/(2cottheta)$

= $\frac{{(\frac{4}{3})}^{2} - 1}{2 \times \frac{4}{3}}$ $((4/3)^2-1)/(2xx4/3)$

= $\frac{\frac{16}{9} - 1}{\frac{8}{3}}$ $(16/9-1)/(8/3)$

= $\frac{\frac{16 - 9}{9}}{\frac{8}{3}}$ $((16-9)/9)/(8/3)$

= $\frac{7}{9} \times \frac{3}{8}$ $7/9xx3/8$

= $7/(3cancel9)xx(1cancel3)/8$

= $7/24$

How do you find the value of cot2thetacot2θcot2theta given cottheta=4/3cotθ=43cottheta=4/3 and pi<theta<(3pi)/2π<θ<3π2pi<theta<(3pi)/2?