This is a free lesson from our course in Trigonometry

 This lesson content introduces and walks you through the important concepts of sum and difference formulas for sine and cosine functions. The purpose and use of the sum, difference formulas have been explained by the instructor using video and with the help of some examples, practice questions with solution. Sine of the quantity (A + B): multiply sin A by cos B and then add the multiplication product of cos A by sin B i.e.      sin (A + B) = sin A cos B + cos A sin B The difference identity i.e. sine of the quantity (A - B) can be worked by multiplying sin A by cos B and then subtracting cos A times sin B:      sin(A - B) = sin A cos B - cos A sin B. (More text below video...)
Other useful lessons:
 Using Sum and Difference Formulas Double and Half Angle Formulas Using Double and Half Angle Formulas
(Continued from above)Similarly, the sum and difference formulas for cosine functions are as below:
cos (A + B) = cos A cos B - sin A sin B
cos (A - B) = cos A cos B + sin A sin B
These formulas can be used to find exact values of trigonometric ratios for the angles. For example, to calculate the exact value of cos 75, first write it as cos (45 + 30), then plug in the values of A = 45 and B = 30 in the formula cos (A + B) = cos A cos B - sin A sin B. The resulting expression is:
cos 75 = cos 45 cos 30 - sin 45 sin 30,
Now plug in the corresponding values for each and you'll get the answer i.e. cos 75 = (6 - 2)/4.
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