Solve an^-11/2+tan^-12/11=tan^-13/4

$$a n ^ { - 1 } \frac { 1 } { 2 } + \tan ^ { - 1 } \frac { 2 } { 11 } = \tan ^ { - 1 } \frac { 3 } { 4 }$$

Solve for a

$$a=-\frac{1322317402704094400000000000000000n}{2769416745436257173725837327803}$$

$$n\neq 0$$

Solution Steps

Evaluate trigonometric functions in the problem

$$a n ^ {-1} \frac{1}{2} + 0.003173336564554377 ^ {-1} = 0.013090717084835085 ^ {-1}$$

Calculate 0.003173336564554377 to the power of -1 and get \frac{1000000000000000000}{3173336564554377}.

$$an^{-1}\times \frac{1}{2}+\frac{1000000000000000000}{3173336564554377}=0.013090717084835085^{-1}$$

Calculate 0.013090717084835085 to the power of -1 and get \frac{200000000000000000}{2618143416967017}.

$$an^{-1}\times \frac{1}{2}+\frac{1000000000000000000}{3173336564554377}=\frac{200000000000000000}{2618143416967017}$$

Subtract \frac{1000000000000000000}{3173336564554377} from both sides.

$$an^{-1}\times \frac{1}{2}=\frac{200000000000000000}{2618143416967017}-\frac{1000000000000000000}{3173336564554377}$$

Subtract \frac{1000000000000000000}{3173336564554377} from \frac{200000000000000000}{2618143416967017} to get -\frac{661158701352047200000000000000000}{2769416745436257173725837327803}.

$$an^{-1}\times \frac{1}{2}=-\frac{661158701352047200000000000000000}{2769416745436257173725837327803}$$

Reorder the terms.

$$\frac{1}{2}\times \frac{1}{n}a=-\frac{661158701352047200000000000000000}{2769416745436257173725837327803}$$

Multiply both sides of the equation by 2n, the least common multiple of 2,n.

$$\frac{1}{2}\times 2\times 1a=-\frac{1322317402704094400000000000000000}{2769416745436257173725837327803}n$$

Multiply \frac{1}{2} and 2 to get 1.

$$1a=-\frac{1322317402704094400000000000000000}{2769416745436257173725837327803}n$$

Reorder the terms.

$$a=-\frac{1322317402704094400000000000000000}{2769416745436257173725837327803}n$$

Solve for n

$$n=-\frac{2769416745436257173725837327803a}{1322317402704094400000000000000000}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$a n ^ {-1} \frac{1}{2} + 0.003173336564554377 ^ {-1} = 0.013090717084835085 ^ {-1}$$

Calculate 0.003173336564554377 to the power of -1 and get \frac{1000000000000000000}{3173336564554377}.

$$an^{-1}\times \frac{1}{2}+\frac{1000000000000000000}{3173336564554377}=0.013090717084835085^{-1}$$

Calculate 0.013090717084835085 to the power of -1 and get \frac{200000000000000000}{2618143416967017}.

$$an^{-1}\times \frac{1}{2}+\frac{1000000000000000000}{3173336564554377}=\frac{200000000000000000}{2618143416967017}$$

Reorder the terms.

$$\frac{1}{2}\times \frac{1}{n}a+\frac{1000000000000000000}{3173336564554377}=\frac{200000000000000000}{2618143416967017}$$

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2n, the least common multiple of 2,n.

$$\frac{1}{2}\times 2\times 1a+2n\times \frac{1000000000000000000}{3173336564554377}=\frac{400000000000000000}{2618143416967017}n$$

Multiply \frac{1}{2} and 2 to get 1.

$$1a+2n\times \frac{1000000000000000000}{3173336564554377}=\frac{400000000000000000}{2618143416967017}n$$

Multiply 2 and \frac{1000000000000000000}{3173336564554377} to get \frac{2000000000000000000}{3173336564554377}.

$$1a+\frac{2000000000000000000}{3173336564554377}n=\frac{400000000000000000}{2618143416967017}n$$

Subtract \frac{400000000000000000}{2618143416967017}n from both sides.

$$1a+\frac{2000000000000000000}{3173336564554377}n-\frac{400000000000000000}{2618143416967017}n=0$$

Combine \frac{2000000000000000000}{3173336564554377}n and -\frac{400000000000000000}{2618143416967017}n to get \frac{1322317402704094400000000000000000}{2769416745436257173725837327803}n.

$$1a+\frac{1322317402704094400000000000000000}{2769416745436257173725837327803}n=0$$

Subtract 1a from both sides. Anything subtracted from zero gives its negation.

$$\frac{1322317402704094400000000000000000}{2769416745436257173725837327803}n=-a$$

Divide both sides of the equation by \frac{1322317402704094400000000000000000}{2769416745436257173725837327803}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{1322317402704094400000000000000000}{2769416745436257173725837327803}n}{\frac{1322317402704094400000000000000000}{2769416745436257173725837327803}}=-\frac{a}{\frac{1322317402704094400000000000000000}{2769416745436257173725837327803}}$$

Dividing by \frac{1322317402704094400000000000000000}{2769416745436257173725837327803} undoes the multiplication by \frac{1322317402704094400000000000000000}{2769416745436257173725837327803}.

$$n=-\frac{a}{\frac{1322317402704094400000000000000000}{2769416745436257173725837327803}}$$

Divide -a by \frac{1322317402704094400000000000000000}{2769416745436257173725837327803} by multiplying -a by the reciprocal of \frac{1322317402704094400000000000000000}{2769416745436257173725837327803}.

$$n=-\frac{2769416745436257173725837327803a}{1322317402704094400000000000000000}$$

Variable n cannot be equal to 0.

$$n=-\frac{2769416745436257173725837327803a}{1322317402704094400000000000000000}\text{, }n\neq 0$$