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