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If tan A + cot A=4, Then prove that Tan^4 A + cot^4 A=194No spam answer please |
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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! |
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