Question

what is the examples of the formula sin(a+b) = sina×cosb+cosa×sinb​

Answer 1

Here are two for the price of one (using Euler's formula):

cos(A+B)+isin(A+B)≡ei(A+B)≡eiA×eiB

cos⁡(A+B)+isin⁡(A+B)≡ei(A+B)≡eiA×eiB

≡[cos(A)+isin(A)][cos(B)+isin(B)]

≡[cos⁡(A)+isin⁡(A)][cos⁡(B)+isin⁡(B)]

≡[cos(A)cos(B)−sin(A)sin(B)]+i[sin(A)cos(B)+cos(A)sin(B)]

≡[cos⁡(A)cos⁡(B)−sin⁡(A)sin⁡(B)]+i[sin⁡(A)cos⁡(B)+cos⁡(A)sin⁡(B)]

Now equate imaginary parts to give the result for sin(A+B)sin⁡(A+B) (and, if you want, equate real parts to give the result for cos(A+B)cos⁡(A+B)).

Answer 2

Answer:

Let you have to find the value of Sin75°

Step-by-step explanation:

#1. Sin(45°+30°)

#2. Sin45°Cos30°+Cos45°Sin30°

#3.1/√2 × √3/2 + 1/√2 ×1/2

#4.√3/2√2