Solve cos^2165-cos15*cos75/cos^215+cos15cos15*tan15

$$\frac { \cos ^ { 2 } 165 - \cos 15 \cdot \cos 75 } { \cos ^ { 2 } 15 + \cos 15 \cos 15 \cdot \tan 15 }$$

Evaluate

$$-\frac{193071796155388135579422682425124}{189656290343246787357171103993675}\approx -1.018008924$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{-0.9659258262890682 ^ {2} - 0.9977052596616622}{0.9659258262890683 ^ {2} + 0.9659258262890683 \cdot 0.9975405722839542}$$

Calculate 0.9659258262890682 to the power of 2 and get 0.93301270189221915579422682425124.

$$\frac{-0.93301270189221915579422682425124-0.9977052596616622}{0.9659258262890683^{2}+0.9659258262890683\times 0.9975405722839542}$$

Subtract 0.9977052596616622 from -0.93301270189221915579422682425124 to get -1.93071796155388135579422682425124.

$$\frac{-1.93071796155388135579422682425124}{0.9659258262890683^{2}+0.9659258262890683\times 0.9975405722839542}$$

Calculate 0.9659258262890683 to the power of 2 and get 0.93301270189221934897939208206489.

$$\frac{-1.93071796155388135579422682425124}{0.93301270189221934897939208206489+0.9659258262890683\times 0.9975405722839542}$$

Multiply 0.9659258262890683 and 0.9975405722839542 to get 0.96355020154024852459231895787186.

$$\frac{-1.93071796155388135579422682425124}{0.93301270189221934897939208206489+0.96355020154024852459231895787186}$$

Add 0.93301270189221934897939208206489 and 0.96355020154024852459231895787186 to get 1.89656290343246787357171103993675.

$$\frac{-1.93071796155388135579422682425124}{1.89656290343246787357171103993675}$$

Expand \frac{-1.93071796155388135579422682425124}{1.89656290343246787357171103993675} by multiplying both numerator and the denominator by 100000000000000000000000000000000.

$$\frac{-193071796155388135579422682425124}{189656290343246787357171103993675}$$

Fraction \frac{-193071796155388135579422682425124}{189656290343246787357171103993675} can be rewritten as -\frac{193071796155388135579422682425124}{189656290343246787357171103993675} by extracting the negative sign.

$$-\frac{193071796155388135579422682425124}{189656290343246787357171103993675}$$