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...)
(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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,
first write it as cos (45
6 -