Question 107

If $$sin θ + cos θ = \sqrt{2} sin (90^{\circ} - θ)$$, then cot θ is equal to

Solution

Expression : $$sin θ + cos θ = \sqrt{2} sin (90^{\circ} - θ)$$

=> $$sin \theta + cos \theta = \sqrt{2} cos \theta$$

=> $$sin \theta = cos \theta (\sqrt{2} - 1)$$

=> $$\frac{cos \theta}{sin \theta} = \frac{1}{\sqrt{2} - 1}$$

=> $$cot \theta = \frac{1}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1}$$

=> $$cot \theta = \sqrt{2} + 1$$

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