Solve -1(1/2)+tan^-1(2/11)=1/2sin^-1(24/25)

$$- 1 ( \frac { 1 } { 2 } ) + \tan ^ { - 1 } ( \frac { 2 } { 11 } ) = \frac { 1 } { 2 } \sin ^ { - 1 } ( \frac { 24 } { 25 } )$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$-1 {(\frac{1}{2})} + 0.003173336564554377 ^ {-1} = \frac{1}{2} 0.01675437686898136 ^ {-1}$$

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

$$-\frac{1}{2}+0.003173336564554377^{-1}=\frac{1}{2}\times 0.01675437686898136^{-1}$$

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

$$-\frac{1}{2}+\frac{1000000000000000000}{3173336564554377}=\frac{1}{2}\times 0.01675437686898136^{-1}$$

Add -\frac{1}{2} and \frac{1000000000000000000}{3173336564554377} to get \frac{1996826663435445623}{6346673129108754}.

$$\frac{1996826663435445623}{6346673129108754}=\frac{1}{2}\times 0.01675437686898136^{-1}$$

Calculate 0.01675437686898136 to the power of -1 and get \frac{12500000000000000}{209429710862267}.

$$\frac{1996826663435445623}{6346673129108754}=\frac{1}{2}\times \frac{12500000000000000}{209429710862267}$$

Multiply \frac{1}{2} and \frac{12500000000000000}{209429710862267} to get \frac{6250000000000000}{209429710862267}.

$$\frac{1996826663435445623}{6346673129108754}=\frac{6250000000000000}{209429710862267}$$

Least common multiple of 6346673129108754 and 209429710862267 is 1329181918366565707698557985318. Convert \frac{1996826663435445623}{6346673129108754} and \frac{6250000000000000}{209429710862267} to fractions with denominator 1329181918366565707698557985318.

$$\frac{418194830765350717146150721007341}{1329181918366565707698557985318}=\frac{39666707056929712500000000000000}{1329181918366565707698557985318}$$

Compare \frac{418194830765350717146150721007341}{1329181918366565707698557985318} and \frac{39666707056929712500000000000000}{1329181918366565707698557985318}.

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