Question

if sina cosa tana are in gp then (cota)^6-(cota)^2 is

Answer 1

Let angle A be 'x'

Gn that

$\sin(x) \: \: \cos(x) \: \: \: \tan(x) \: \: \: are \: in \: gp$
Therefore,

$\frac{ \cos(x) }{ \sin(x) } = \frac{ \tan(x) }{ \cos(x) }$
since it's common ratio 'r' is constant

ie
$\tan(x) = \frac{ \tan(x) }{ \cos(x) }$
ie
$\cos(x) = 1$
》 x = 0° ( cos 0° = 1)

Therefore

${ \cot(x) }^{6} - { \cot(x) }^{2} = { \cot(0) }^{6} - { \cot(x) }^{2}$