Solve cos^{2}10^{circ}+cos^250^circ+cos^270^circ=3/2

$$\cos ^ { 2 } 10 ^ { \circ } + \cos ^ { 2 } 50 ^ { \circ } + \cos ^ { 2 } 70 ^ { \circ } = \frac { 3 } { 2 }$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$0.984807753012208 ^ {2} + 0.6427876096865394 ^ {2} + 0.3420201433256688 ^ {2} = \frac{3}{2}$$

Calculate 0.984807753012208 to the power of 2 and get 0.969846310392954075097397035264.

$$0.969846310392954075097397035264+0.6427876096865394^{2}+0.3420201433256688^{2}=\frac{3}{2}$$

Calculate 0.6427876096865394 to the power of 2 and get 0.41317591116653492029192554775236.

$$0.969846310392954075097397035264+0.41317591116653492029192554775236+0.3420201433256688^{2}=\frac{3}{2}$$

Add 0.969846310392954075097397035264 and 0.41317591116653492029192554775236 to get 1.38302222155948899538932258301636.

$$1.38302222155948899538932258301636+0.3420201433256688^{2}=\frac{3}{2}$$

Calculate 0.3420201433256688 to the power of 2 and get 0.11697777844051102819933696729344.

$$1.38302222155948899538932258301636+0.11697777844051102819933696729344=\frac{3}{2}$$

Add 1.38302222155948899538932258301636 and 0.11697777844051102819933696729344 to get 1.5000000000000000235886595503098.

$$1.5000000000000000235886595503098=\frac{3}{2}$$

Convert decimal number 1.5000000000000000235886595503098 to fraction \frac{7500000000000000117943297751549}{10000000000}. Reduce the fraction \frac{7500000000000000117943297751549}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{7500000000000000117943297751549}{5000000000000000000000000000000}=\frac{3}{2}$$

Least common multiple of 5000000000000000000000000000000 and 2 is 5000000000000000000000000000000. Convert \frac{7500000000000000117943297751549}{5000000000000000000000000000000} and \frac{3}{2} to fractions with denominator 5000000000000000000000000000000.

$$\frac{7500000000000000117943297751549}{5000000000000000000000000000000}=\frac{7500000000000000000000000000000}{5000000000000000000000000000000}$$

Compare \frac{7500000000000000117943297751549}{5000000000000000000000000000000} and \frac{7500000000000000000000000000000}{5000000000000000000000000000000}.

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