Question

If sintheta +costheta = √2 sin (90 - theta) determine cot theta

Answer 1

Step-by-step explanation:

your answer is in the above attachment

Answer 2

Answer:

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

Step-by-step explanation:

Given ,

$\sin \theta + \cos \theta = \sqrt{2} \sin(90 \degree - \theta) \\ \\ \implies \sin \theta + \cos \theta = \sqrt{2} \cos \theta \\ \\ \implies \sin \theta = \sqrt{2} \cos \theta - \cos \theta \\ \\ \implies \sin \theta = \cos \theta( \sqrt{2} - 1) \\ \\ \implies \frac{ \sin \theta }{ \sqrt{2} - 1 } = \cos \theta \\ \\ \implies \frac{1}{ \sqrt{2} - 1 } = \frac{ \cos \theta}{ \sin \theta } \\ \\ \implies \cot \theta = \frac{1}{ \sqrt{2} - 1} \\ \\ \implies \cot \theta = \frac{ \sqrt{2} + 1}{( \sqrt{2} - 1)( \sqrt{2} + 1) } \\ \\ \implies \cot \theta = \frac{ \sqrt{2} + 1}{ { (\sqrt{2}) }^{2} - {1}^{2} } \\ \\ \implies \cot \theta = \frac{ \sqrt{2} + 1 }{2 - 1} \\ \\ \implies \cot \theta = \sqrt{2} + 1$