Question

T
If tan 8theta = cot 2theta, where 0 < 80 <
2
then what is the value of tan 5theta
​

Answer 1

$\large\underline{\sf{Solution-}}$

It is given that

$\rm :\longmapsto\:0 < \theta \: < 90$

and

$\rm :\longmapsto\:tan8\theta = cot2\theta$

$\rm :\longmapsto\:tan8\theta = tan(90 - 2\theta)$

$\rm :\longmapsto\:8\theta = 90 - 2\theta$

$\rm :\longmapsto\:8\theta + 2\theta = 90$

$\rm :\longmapsto\:10\theta = 90$

$\rm :\longmapsto\:\theta = 9$

So,

$\rm :\longmapsto\:tan5\theta$

$\rm \: = \: tan(9 \times 5)$

$\rm \: = \: tan45$

$\rm \: = \: 1$