Solve frac{cos^{2}5^{circ}-sin^25^circ}{sin40^circcos40^circ}=

$$\frac { \cos ^ { 2 } 5 ^ { \circ } - \sin ^ { 2 } 5 ^ { \circ } } { \sin 40 ^ { \circ } \cos 40 ^ { \circ } } =$$

Evaluate

$$\frac{9848077530122079956427182176025011}{4924038765061039868913949728354000}\approx 2$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.9961946980917455 ^ {2} - 0.08715574274765817 ^ {2}}{0.6427876096865393 \cdot 0.766044443118978}$$

Calculate 0.9961946980917455 to the power of 2 and get 0.99240387650610396533913523677025.

$$\frac{0.99240387650610396533913523677025-0.08715574274765817^{2}}{0.6427876096865393\times 0.766044443118978}$$

Calculate 0.08715574274765817 to the power of 2 and get 0.0075961234938959696964170191677489.

$$\frac{0.99240387650610396533913523677025-0.0075961234938959696964170191677489}{0.6427876096865393\times 0.766044443118978}$$

Subtract 0.0075961234938959696964170191677489 from 0.99240387650610396533913523677025 to get 0.9848077530122079956427182176025011.

$$\frac{0.9848077530122079956427182176025011}{0.6427876096865393\times 0.766044443118978}$$

Multiply 0.6427876096865393 and 0.766044443118978 to get 0.4924038765061039868913949728354.

$$\frac{0.9848077530122079956427182176025011}{0.4924038765061039868913949728354}$$

Expand \frac{0.9848077530122079956427182176025011}{0.4924038765061039868913949728354} by multiplying both numerator and the denominator by 10000000000000000000000000000000000.

$$\frac{9848077530122079956427182176025011}{4924038765061039868913949728354000}$$