Question

Two angles of a triangle are cot inverse 2 and cot inverse 3 than the third angle is

Answer 1

Answer:

The third angle is \frac{3\pi}{4}

Step-by-step explanation:

Formula used:

cot^{-1}x=tan^{-1}(\frac{1}{x})

tan^{-1}x+tan^{-1}y=tan^{-1}(\frac{x+y}{1-xy})

Let the three angles of a triangle be

A,B and C

Then,

A+B+C=\pi

cot^{-1}2+cot^{-1}3+C=\pi

tan^{-1}(\frac{1}{2})+tan^{-1}(\frac{1}{3})+C=\pi

tan^{-1}(\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2}.\frac{1}{3}})+C=\pi

tan^{-1}(\frac{\frac{3+2}{6}}{1-\frac{1}{6}})+C=\pi

tan^{-1}(\frac{\frac{5}{6}}{\frac{5}{6}})+C=\pi

tan^{-1}(1)+C=\pi

\frac{\pi}{4}+C=\pi

C=\pi-\frac{\pi}{4}

C=\frac{3\pi}{4}

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