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# Trigonomentry Question

If sin A , cos A , tan A are in Geometric Progression . then $$cot^{6} A - cot^{2}$$

the answer is 1

I wanted to know how? please Explain!

Note by Vamsi Krishna Appili
4 years, 1 month ago

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$$cos^{2}A=\frac{sin^{2}A}{cosA},\Rightarrow cot^{2}A=\frac{1}{cosA}.$$As in question $$cot^{6}A-cot^{2}A = \frac{1-cos^{2}A}{cos^{3}A} = \frac{sin^{2}A}{cos^{3}A} = 1.$$ · 4 years, 1 month ago

right · 4 years, 1 month ago

Comment deleted Jul 14, 2013

Bt this is no harmonic progression man.. · 4 years, 1 month ago

but it is not in hp it is in gp frnd · 4 years, 1 month ago

dear vamsi ,plz match the question and then post · 4 years, 1 month ago

cos^2x=sin^2x!!!! Hence, cot^6x=cosec^2x!!! Therefore, by identity cosec^2x-cot^2x=1!!!! · 4 years, 1 month ago

Calm down, that was understood without those exclamations also! · 4 years, 1 month ago

what is this ^ ? · 4 years, 1 month ago

^ means a number raised to some power like 2^2 means $\ 2^2$ · 4 years, 1 month ago