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If tan A + cot A = 4, then tan⁴A + cot⁴A =

Posted by Manoranjan A 5 years, 10 months ago

CBSE > Class 10 > Mathematics

3 answers

Bhavya Saini 5 years, 10 months ago

Given Equation is tanA + cotA = 4. On squaring both sides, we get = > (tanA + cotA)^2 = (4)^2 = > tan^2A + cot^2A + 2tanAcotA = 16 = > tan^2A + cot^2A + 2 * tanA * (1/tanA) = 16 = > tan^2A + cot^2A + 2 = 16 = > tan^2A + cot^2A = 16 - 2 = > tan^2A + cot^2A = 14. On squaring both sides, we get = > (tan^2A + cot^2A)^2 = (14)^2 = > tan^4A + cot^4A + 2 * tan^4A * cot^4a = 196 = > tan^4A + cot^4A + 2 * tan^4A * (1/tan^4A) = 196 = > tan^4A + cot^4A + 2 = 196 = > tan^4A + cot^4A = 196 - 2 = > tan^4A + cot^4A = 194. Hope this helps

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Madhu Sharma 5 years, 10 months ago

Just square both the side twice

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Madhu Sharma 5 years, 10 months ago

Answer is 574

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