Trigonomentry Question

If sin A , cos A , tan A are in Geometric Progression . then cot6Acot2cot^{6} A - cot^{2}

the answer is 1

I wanted to know how? please Explain!

Note by Vamsi Krishna Appili
6 years, 1 month ago

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8 votes

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cos2A=sin2AcosA,cot2A=1cosA.cos^{2}A=\frac{sin^{2}A}{cosA},\Rightarrow cot^{2}A=\frac{1}{cosA}.As in question cot6Acot2A=1cos2Acos3A=sin2Acos3A=1.cot^{6}A-cot^{2}A = \frac{1-cos^{2}A}{cos^{3}A} = \frac{sin^{2}A}{cos^{3}A} = 1.

Kishan k - 6 years, 1 month ago

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right

Anubhav Singh - 6 years, 1 month ago

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dear vamsi ,plz match the question and then post

Shubham Gupta - 6 years, 1 month ago

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cos^2x=sin^2x!!!! Hence, cot^6x=cosec^2x!!! Therefore, by identity cosec^2x-cot^2x=1!!!!

Subhrodipto Basu Choudhury - 6 years, 1 month ago

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Calm down, that was understood without those exclamations also!

Akshat Jain - 6 years, 1 month ago

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what is this ^ ?

Devashish Sharma - 6 years, 1 month ago

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^ means a number raised to some power like 2^2 means  22\ 2^2

Cody Martin - 6 years, 1 month ago

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