If $sin A, cos A$ and $tan A$ are in geometric progression, then $cot^{6} A - cot^{2} A = ........$

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sin A, cos A

and

tan A

are in geometric progression, then

cot^{6} A - cot^{2} A = ........

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

sice $sin A . cos A$ and $tan A$ are G.P. we have $cos^{2} A = sin A tan A$
$\Rightarrow cot^{2} A = sec A \Rightarrow cot^{4} A = 1 + tan^{2} A$
$\Rightarrow cot^{6} A - cot^{2} A = 1$

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Question Text	If $sin A, cos A$ and $tan A$ are in geometric progression, then $cot^{6} A - cot^{2} A = ........$
Answer Type	Text solution:1
Upvotes	150

If sinA,cosA and tanA are in geometric progression, then cot6A−cot2A=........

Text solutionVerified

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If $sin A, cos A$ and $tan A$ are in geometric progression, then $cot^{6} A - cot^{2} A = ........$