Respuesta :
Answer:
[tex]\sin(\frac{\pi}{7}+x)[/tex]
Step-by-step explanation:
We are going to use the identity
[tex]\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)[/tex]
because this identities right hand side matches your expression where
[tex]a=\frac{\pi}{7}[/tex] and [tex]b=x[/tex].
So we have that [tex]\sin(\frac{\pi}{7})\cos(x)+\cos(\frac{\pi}{7})\sin(x)[/tex] is equal to [tex]\sin(\frac{\pi}{7}+x)[/tex].
The given expression is written as sin(π/7 + x). Using sine of compound angle identity it is obtained.
What are compound angle identities for sine and cosine?
A compound angle is the sum of two or more angles. Consider A and B are two angles. Where their compound angle becomes A + B. So, the sine and cosine of this compound angle are
1) sin (A + B) = sin A cos B + cos A sin B
2) sin (A - B) = sin A cos B - cos A sin B
3) cos (A + B) = cos A cos B - sin A sin B
4) cos (A - B) = cos A cos B + sin A sin B
Calculation:
The given expression is sin(π/7) cos(x) + cos(π/7) sin(x)
This is in the form of sin A cos B + cos A sin B
where A = π/7 and B = x
So, using the above identity we can write,
sin(π/7) cos(x) + cos(π/7) sin(x) = sin(π/7 + x)
Thus, the given expression is expressed in the angle of sine. I.e., sin(π/7 + x).
Learn more about trigonometric identities here:
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