Question

cos theta+ sin theta=root 2 what is the value of 1/tan theta

Answer 1

i dont think it makes any sense

Answer 2

           

$\huge\boxed{\ \ \ \ \ \ \ \ \ \ \huge\boxed{\ \ \ \ \ \ \ \ \ \ \huge\boxed{\ \ \ \ \ \bold{\frac{1}{\tan\theta}=1}\ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ }$

$\sin\theta+\cos\theta=\sqrt{2} \\ \\ \\ (\sin\theta+\cos\theta)^2=(\sqrt{2})^2 \\ \\ \sin^2\theta+\cos^2\theta+2\sin\theta \cdot \cos\theta=2 \\ \\ 1+2\sin\theta \cdot \cos\theta=2 \\ \\ 2\sin\theta \cdot \cos\theta=1 \\ \\ 4\sin\theta \cdot \cos\theta=2$

$\sin^2\theta+\cos^2\theta+2\sin\theta \cdot \cos\theta-4 \sin\theta \cdot \cos\theta=2-4 \sin\theta \cdot \cos\theta \\ \\ \sin^2\theta+\cos^2\theta-2\sin\theta \cdot \cos\theta=2-2 \\ \\ (\sin\theta-\cos\theta)^2=0 \\ \\ \sin\theta-\cos\theta=0 \\ \\ \sin\theta=\cos\theta \\ \\ \frac{\sin\theta}{\sin\theta}=\frac{\cos\theta}{\sin\theta} \\ \\ \bold{1}=\frac{1}{\tan\theta}$

$\therefore\ \frac{1}{\tan\theta}=\bold{1} \\ \\ \\ \sf{Here,} \ \ \theta =(45+180n) \textdegree,\ \sf{for whole numbers} \ n. \\ \\ \\ \\ \sf{Hope this helps. Plz mark it as the brainliest. \\ \\ \\ Thank you. :-)}$