Solve sin^-1(1/sqrt{10})+sin^-1(1/sqrt{3})=pi/4

$$\sin ^ { - 1 } ( \frac { 1 } { \sqrt { 10 } } ) + \sin ^ { - 1 } ( \frac { 1 } { \sqrt { 3 } } ) = \frac { \pi } { 4 }$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$0.0055191876824419546 ^ {-1} + 0.010076492606215638 ^ {-1} = \frac{\pi}{4}$$

Multiply both sides of the equation by 4.

$$4\times 0.0055191876824419546^{-1}+4\times 0.010076492606215638^{-1}=\pi$$

Calculate 0.0055191876824419546 to the power of -1 and get \frac{5000000000000000000}{27595938412209773}.

$$4\times \frac{5000000000000000000}{27595938412209773}+4\times 0.010076492606215638^{-1}=\pi$$

Multiply 4 and \frac{5000000000000000000}{27595938412209773} to get \frac{20000000000000000000}{27595938412209773}.

$$\frac{20000000000000000000}{27595938412209773}+4\times 0.010076492606215638^{-1}=\pi$$

Calculate 0.010076492606215638 to the power of -1 and get \frac{500000000000000000}{5038246303107819}.

$$\frac{20000000000000000000}{27595938412209773}+4\times \frac{500000000000000000}{5038246303107819}=\pi$$

Multiply 4 and \frac{500000000000000000}{5038246303107819} to get \frac{2000000000000000000}{5038246303107819}.

$$\frac{20000000000000000000}{27595938412209773}+\frac{2000000000000000000}{5038246303107819}=\pi$$

Add \frac{20000000000000000000}{27595938412209773} and \frac{2000000000000000000}{5038246303107819} to get \frac{155956802886575926000000000000000000}{139035134686106945361385264515087}.

$$\frac{155956802886575926000000000000000000}{139035134686106945361385264515087}=\pi$$

Compare \frac{155956802886575926000000000000000000}{139035134686106945361385264515087} and \pi .

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