Question 104

If Θ is a positive acute angle and tan Θ+ cot Θ = 2, then the value of sec 0 is

Solution

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

=> $$tan \theta + \frac{1}{tan \theta} = 2$$

=> $$tan^2 \theta - 2tan \theta + 1 = 0$$

=> $$(tan \theta - 1)^2 = 0$$

=> $$tan \theta = 1$$

$$\therefore sec\theta = \sqrt{1 + tan^2 \theta}$$

= $$\sqrt{1 + 1} = \sqrt{2}$$

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