Question

if tanA + cotA =4 than tan⁴A+ cot⁴A is equal to​

Answer 1

Answer:

194

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 = 194.