Solve n^-15/13+cos^-13/5=tan^-163/16

$$n ^ { - 1 } \frac { 5 } { 13 } + \cos ^ { - 1 } \frac { 3 } { 5 } = \tan ^ { - 1 } \frac { 63 } { 16 }$$

Solve for n

$$n=\frac{1720673910030821153321834476077}{60522438530557724500000000000000}\approx 0.028430347$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$n ^ {-1} \frac{5}{13} + 0.9999451693655121 ^ {-1} = 0.0688307304338548 ^ {-1}$$

Calculate 0.9999451693655121 to the power of -1 and get \frac{10000000000000000}{9999451693655121}.

$$n^{-1}\times \frac{5}{13}+\frac{10000000000000000}{9999451693655121}=0.0688307304338548^{-1}$$

Calculate 0.0688307304338548 to the power of -1 and get \frac{2500000000000000}{172076826084637}.

$$n^{-1}\times \frac{5}{13}+\frac{10000000000000000}{9999451693655121}=\frac{2500000000000000}{172076826084637}$$

Subtract \frac{10000000000000000}{9999451693655121} from both sides.

$$n^{-1}\times \frac{5}{13}=\frac{2500000000000000}{172076826084637}-\frac{10000000000000000}{9999451693655121}$$

Subtract \frac{10000000000000000}{9999451693655121} from \frac{2500000000000000}{172076826084637} to get \frac{23277860973291432500000000000000}{1720673910030821153321834476077}.

$$n^{-1}\times \frac{5}{13}=\frac{23277860973291432500000000000000}{1720673910030821153321834476077}$$

Multiply both sides by \frac{13}{5}, the reciprocal of \frac{5}{13}.

$$n^{-1}=\frac{23277860973291432500000000000000}{1720673910030821153321834476077}\times \frac{13}{5}$$

Multiply \frac{23277860973291432500000000000000}{1720673910030821153321834476077} and \frac{13}{5} to get \frac{60522438530557724500000000000000}{1720673910030821153321834476077}.

$$n^{-1}=\frac{60522438530557724500000000000000}{1720673910030821153321834476077}$$

Reorder the terms.

$$\frac{1}{n}=\frac{60522438530557724500000000000000}{1720673910030821153321834476077}$$

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 1720673910030821153321834476077n, the least common multiple of n,1720673910030821153321834476077.

$$1720673910030821153321834476077=60522438530557724500000000000000n$$

Swap sides so that all variable terms are on the left hand side.

$$60522438530557724500000000000000n=1720673910030821153321834476077$$

Divide both sides by 60522438530557724500000000000000.

$$n=\frac{1720673910030821153321834476077}{60522438530557724500000000000000}$$