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If tan A + cot A = 4, then tan⁴A + cot⁴A = |
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Answer» 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 Just square both the side twice Answer is 574 |
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