Question

If sin theta + cos theta = root2, then evaluate tan theta + cot theta

Answer 1

$\displaystyle\\\\\sin\theta+\cos\theta= \sqrt{2}\\\\\sin\theta+\cos\theta= 2\times\frac{\sqrt{2}}{2}\\\\\implies~~\sin\theta=\cos\theta= \frac{\sqrt{2}}{2}\\\\\implies~~\theta=45^o\\\\\implies~~\tan\theta + \cot\theta=\tan45^o + \cot45^o=1+1=\boxed{\bf2}$

Answer 2

sin theta + cos theta = root2

Squaring both sides:

(sin theta + cos theta)^2  = 2

sin^2 theta + cos^2 theta + 2 sin theta cos theta = 2

1 + sin 2theta = 2

sin 2theta = 1

2 theta = 90

theta = 45

so tan theta + cot theta = 1 + 1

= 2