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in Trigonometry by (15 points)
edited by

If θ is an acute angle and tanθ + cotθ = 2, find the value of tan7 θ + cot7 θ.

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1 Answer

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It is given that, tanθ + cotθ = 2

⇒ tanθ + \(\frac{1}{tanθ}\) = 2

⇒ tan2θ + 1 = 2tanθ

⇒tan2θ - 2tanθ + 1 = 0

⇒(tanθ - 1)2 = 0

⇒ tanθ = 1

so, cotθ = \(\frac{1}{tanθ}\) = 1

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