Question

Cos105-sin195+sin (-135)-cos 135

Answer 1

Cos(90+15)-sin(180+15)-sin(180-45)-cos(180-45)=
=-sin15+sin15-sin45+cos45=-√2/2+√2/2=0

Answer 2

To evaluate the expression cos(105) - sin(195) + sin(-135) - cos(135), we can break it down step by step:

1. Evaluating cos(105): The cosine function calculates the ratio of the adjacent side to the hypotenuse in a right triangle. In this case, we need to convert the angle 105 degrees to radians and then find the cosine value. cos(105) ≈ -0.2588

2. Evaluating sin(195): The sine function calculates the ratio of the opposite side to the hypotenuse in a right triangle. Similarly, we need to convert the angle 195 degrees to radians and then find the sine value. sin(195) ≈ -0.9997

3. Evaluating sin(-135): The sine function is an odd function, which means sin(-x) = -sin(x). So, we can rewrite sin(-135) as -sin(135). Again, we need to convert the angle 135 degrees to radians and find the sine value. sin(-135) ≈ -0.7071

4. Evaluating cos(135): The cosine function is an even function, which means cos(-x) = cos(x). So, cos(135) is the same as cos(-135). Once again, we convert the angle 135 degrees to radians and find the cosine value. cos(135) ≈ -0.7071

Now, substituting these values back into the original expression: cos(105) - sin(195) + sin(-135) - cos(135) ≈ -0.2588 - (-0.9997) + (-0.7071) - (-0.7071)

Simplifying further: -0.2588 + 0.9997 + (-0.7071) + 0.7071 ≈ 0.7419

Therefore, the value of the expression cos(105) - sin(195) + sin(-135) - cos(135) is approximately 0.7419.