Question 177

If tan θ + cot θ = 5, then $$tan^2 θ + cot^2 θ$$ is

Solution

Expression : $$tan\theta + cot\theta = 5$$

Squaring both sides, we get :

=> $$tan^2\theta + cot^2\theta + 2tan\theta cot\theta = 25$$

We know that, $$tan\theta cot\theta = 1$$

=> $$tan^2\theta + cot^2\theta = 25-2 = 23$$

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