Question 140

If tan θ + cot θ = 2, then the value of $$tan^2\theta+cot^2\theta$$ is

Solution

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

Using, $$(x+y)^2=x^2+y^2+2xy$$

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

Also, $$\because tan\theta=\frac{1}{cot\theta}$$

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

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

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

=> Ans - (A)

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