Question

If $\sin \theta ,\cos \theta ,\tan \theta$ are G.P. then the value ${\tan }^6\theta +{\tan }^4\theta =$

• A. $1$
• B. $2$
• C. $4$
• D. $3$

Answer 1

Answer: (A)

$1$

Given,

$\sin \theta ,\cos \theta ,\tan \theta$ are G.P

Then, we've,

${\cos }^2\theta =\sin \theta .\tan \theta$

or, $\cot \theta .\cos \theta =\tan \theta$

or, ${\tan }^2\theta =\cos \theta$......(1) and ${\tan }^3\theta =\sin \theta$.....(2).[ Multiplying both sides of (1) with $\tan \theta$]

Now,

${\tan }^6\theta +{\tan }^4\theta$

$=({\tan }^3\theta {)}^2+({\tan }^2\theta {)}^2$

$={\sin }^2\theta +{\cos }^2\theta$[ Using (1) and (2)]

$=1$.