Question 14

If tanθ+cotθ = 2 then the value of $$tan^nθ + cot^nθ$$ is

Solution

Given : $$tan\theta+cot\theta=2$$

Squaring both sides

=> $$(tan\theta+cot\theta)^2=(2)^2$$

=> $$tan^2\theta+cot^2\theta+2.tan\theta.cot\theta=4$$

$$\because (tan\theta.cot\theta=1)$$

=> $$tan^2\theta+cot^2\theta=4-2=2$$

Again squaring both sides, we get : $$tan^4\theta+cot^4\theta=2$$

Thus, $$tan^n\theta+cot^n\theta=2$$

=> Ans - (D)

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