Differentiate Cos25º - Sin 25º

In order to differentiate the expression Cos25º - Sin25º, we must first understand that differentiating trigonometric functions involves the application of standard differentiation formulas. In calculus, the derivatives of trigonometric functions are well-defined. Let's go through the differentiation step-by-step:

The formula for finding the derivative of the cosine function is that the derivative of cos(u) is -sin(u). Hence, for Cos25º, the derivative would be:

-Sin25º

Similarly, the formula for finding the derivative of the sine function is that the derivative of sin(u) is cos(u). Thus, for Sin25º, the derivative would be:

Cos25º

When we differentiate the whole expression Cos25º - Sin25º, we apply these rules:

d/dx [Cos25º - Sin25º] = d/dx [Cos25º] - d/dx [Sin25º]

Plugging in the derivatives from above gives us:

-Sin25º - Cos25º

Thus, the differentiated expression for Cos25º - Sin25º is - (Sin25º + Cos25º). This simplified expression matches one of the provided options. Therefore, the differentiated expression results in:

- ( Sin25º + Cos25º)