How to solve cot((7pi)/4)

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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$$ctg\frac{7\pi}{4}$$

$-1$

Use $\cot(x+y)=\frac{\cot(x)\cot(y)-1}{\cot(y)+\cot(x)}$ where $x=\frac{3\pi }{2}$ and $y=\frac{\pi }{4}$ to obtain the result.

$$\cot(\frac{3\pi }{2}+\frac{\pi }{4})=\frac{\cot(\frac{3\pi }{2})\cot(\frac{\pi }{4})-1}{\cot(\frac{\pi }{4})+\cot(\frac{3\pi }{2})}$$

Get the value of $\cot(\frac{3\pi }{2})$ from trigonometric values table. Replace the value in both the numerator and the denominator.

$$\frac{0\cot(\frac{\pi }{4})-1}{\cot(\frac{\pi }{4})+0}$$

Get the value of $\cot(\frac{\pi }{4})$ from trigonometric values table. Replace the value in both the numerator and the denominator.

$$\frac{0\times 1-1}{1+0}$$

Do the calculations.

$$-1$$

$-1$