Solve frac{sin^{2}15^{circ}+sin^{2}75^{circ}}{cos^236^circ+cos^254^circ}

$$\frac { \sin ^ { 2 } 15 ^ { \circ } + \sin ^ { 2 } 75 ^ { \circ } } { \cos ^ { 2 } 36 ^ { \circ } + \cos ^ { 2 } 54 ^ { \circ } }$$

Evaluate

$$\frac{1250000000000000017536111480243797}{1250000000000000110643998177474825}\approx 1$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.25881904510252074 ^ {2} + 0.9659258262890683 ^ {2}}{0.8090169943749475 ^ {2} + 0.5877852522924731 ^ {2}}$$

Calculate 0.25881904510252074 to the power of 2 and get 0.0669872981077806650494971021301476.

$$\frac{0.0669872981077806650494971021301476+0.9659258262890683^{2}}{0.8090169943749475^{2}+0.5877852522924731^{2}}$$

Calculate 0.9659258262890683 to the power of 2 and get 0.93301270189221934897939208206489.

$$\frac{0.0669872981077806650494971021301476+0.93301270189221934897939208206489}{0.8090169943749475^{2}+0.5877852522924731^{2}}$$

Add 0.0669872981077806650494971021301476 and 0.93301270189221934897939208206489 to get 1.0000000000000000140288891841950376.

$$\frac{1.0000000000000000140288891841950376}{0.8090169943749475^{2}+0.5877852522924731^{2}}$$

Calculate 0.8090169943749475 to the power of 2 and get 0.65450849718747383485621562775625.

$$\frac{1.0000000000000000140288891841950376}{0.65450849718747383485621562775625+0.5877852522924731^{2}}$$

Calculate 0.5877852522924731 to the power of 2 and get 0.34549150281252625365898291422361.

$$\frac{1.0000000000000000140288891841950376}{0.65450849718747383485621562775625+0.34549150281252625365898291422361}$$

Add 0.65450849718747383485621562775625 and 0.34549150281252625365898291422361 to get 1.00000000000000008851519854197986.

$$\frac{1.0000000000000000140288891841950376}{1.00000000000000008851519854197986}$$

Expand \frac{1.0000000000000000140288891841950376}{1.00000000000000008851519854197986} by multiplying both numerator and the denominator by 10000000000000000000000000000000000.

$$\frac{10000000000000000140288891841950376}{10000000000000000885151985419798600}$$

Reduce the fraction \frac{10000000000000000140288891841950376}{10000000000000000885151985419798600} to lowest terms by extracting and canceling out 8.

$$\frac{1250000000000000017536111480243797}{1250000000000000110643998177474825}$$