Solve {left(sin(3/5)right)}^-1+{left(cos(12/13)right)}^-1={left(cos(33/65)right)}^-1

$${ \left( \sin ( \frac{ 3 }{ 5 } ) \right) }^{ -1 } + { \left( \cos ( \frac{ 12 }{ 13 } ) \right) }^{ -1 } = { \left( \cos ( \frac{ 33 }{ 65 } ) \right) }^{ -1 }$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$0.010471784116245792 ^ {-1} + 0.9998702249713747 ^ {-1} = 0.999960742461578 ^ {-1}$$

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

$$\frac{31250000000000000}{327243253632681}+0.9998702249713747^{-1}=0.999960742461578^{-1}$$

Calculate 0.9998702249713747 to the power of -1 and get \frac{10000000000000000}{9998702249713747}.

$$\frac{31250000000000000}{327243253632681}+\frac{10000000000000000}{9998702249713747}=0.999960742461578^{-1}$$

Add \frac{31250000000000000}{327243253632681} and \frac{10000000000000000}{9998702249713747} to get \frac{315731877839881403750000000000000}{3272007856300733825150134165707}.

$$\frac{315731877839881403750000000000000}{3272007856300733825150134165707}=0.999960742461578^{-1}$$

Calculate 0.999960742461578 to the power of -1 and get \frac{500000000000000}{499980371230789}.

$$\frac{315731877839881403750000000000000}{3272007856300733825150134165707}=\frac{500000000000000}{499980371230789}$$

Compare \frac{315731877839881403750000000000000}{3272007856300733825150134165707} and \frac{500000000000000}{499980371230789}.

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