If tan A + cot A=4, Then prove that Tan^4 A + cot^4 A=194
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Answers
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!
Answer:
Step-by-step explanation:
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