Solve sin^254^circ+cos^272^circ=3/4

$$\sin ^ { 2 } 54 ^ { \circ } + \cos ^ { 2 } 72 ^ { \circ } = \frac { 3 } { 4 }$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$0.8090169943749475 ^ {2} + 0.30901699437494745 ^ {2} = \frac{3}{4}$$

Calculate 0.8090169943749475 to the power of 2 and get 0.65450849718747383485621562775625.

$$0.65450849718747383485621562775625+0.30901699437494745^{2}=\frac{3}{4}$$

Calculate 0.30901699437494745 to the power of 2 and get 0.0954915028125263039545161902615025.

$$0.65450849718747383485621562775625+0.0954915028125263039545161902615025=\frac{3}{4}$$

Add 0.65450849718747383485621562775625 and 0.0954915028125263039545161902615025 to get 0.7500000000000001388107318180177525.

$$0.7500000000000001388107318180177525=\frac{3}{4}$$

Convert decimal number 0.7500000000000001388107318180177525 to fraction \frac{300000000000000055524292727207101}{10000000000}. Reduce the fraction \frac{300000000000000055524292727207101}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{300000000000000055524292727207101}{400000000000000000000000000000000}=\frac{3}{4}$$

Least common multiple of 400000000000000000000000000000000 and 4 is 400000000000000000000000000000000. Convert \frac{300000000000000055524292727207101}{400000000000000000000000000000000} and \frac{3}{4} to fractions with denominator 400000000000000000000000000000000.

$$\frac{300000000000000055524292727207101}{400000000000000000000000000000000}=\frac{300000000000000000000000000000000}{400000000000000000000000000000000}$$

Compare \frac{300000000000000055524292727207101}{400000000000000000000000000000000} and \frac{300000000000000000000000000000000}{400000000000000000000000000000000}.

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