Solve -1(8/17)+sin^-1(3/5)=sin^-1(77/85)

$$- 1 ( \frac { 8 } { 17 } ) + \sin ^ { - 1 } ( \frac { 3 } { 5 } ) = \sin ^ { - 1 } ( \frac { 77 } { 85 } )$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$-1 {(\frac{8}{17})} + 0.010471784116245792 ^ {-1} = 0.015809970989745313 ^ {-1}$$

Multiply -1 and \frac{8}{17} to get -\frac{8}{17}.

$$-\frac{8}{17}+0.010471784116245792^{-1}=0.015809970989745313^{-1}$$

Calculate 0.010471784116245792 to the power of -1 and get \frac{31250000000000000}{327243253632681}.

$$-\frac{8}{17}+\frac{31250000000000000}{327243253632681}=0.015809970989745313^{-1}$$

Add -\frac{8}{17} and \frac{31250000000000000}{327243253632681} to get \frac{528632053970938552}{5563135311755577}.

$$\frac{528632053970938552}{5563135311755577}=0.015809970989745313^{-1}$$

Calculate 0.015809970989745313 to the power of -1 and get \frac{1000000000000000000}{15809970989745313}.

$$\frac{528632053970938552}{5563135311755577}=\frac{1000000000000000000}{15809970989745313}$$

Least common multiple of 5563135311755577 and 15809970989745313 is 87953007890883420097566137360601. Convert \frac{528632053970938552}{5563135311755577} and \frac{1000000000000000000}{15809970989745313} to fractions with denominator 87953007890883420097566137360601.

$$\frac{8357657437530017098262910053006776}{87953007890883420097566137360601}=\frac{5563135311755577000000000000000000}{87953007890883420097566137360601}$$

Compare \frac{8357657437530017098262910053006776}{87953007890883420097566137360601} and \frac{5563135311755577000000000000000000}{87953007890883420097566137360601}.

$$\text{false}$$