Question

if tan alpha + cot alpha = a, then the value of tan^4 alpha + cot^4 alpha is equal to?.




please help me out ​

Answer 1

Solution :

tan alpha + cot a = a

We have to find the value of tan⁴alpha + cot⁴ alpha.

Suppose that tan alpha = x .

cot alpha is 1/x .

We have to find the value of x⁴ + 1/x⁴

x + 1/x = a

> x² + 1/x² + 2 = a²

> x² + 1/x² = a² - 2

> x⁴ + 1/x⁴ + 2(x²)(1/x²) = a⁴ + 4 - 2a²

> x⁴ + 1/x⁴ + 2 = a⁴ - 2a² + 4

> x⁴ + 1/x⁴ = a⁴ - 2a² + 2

Answer : This is equal to a⁴ - 2a² + 2 .

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Answer 2

Answer:

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