watz the value of (sin 5A)/(sin A)?
I would leave it as is
Any attempt to express it in terms of sin A only would only look much more complicated.
Just don't do anything silly such as
sin 5A/sinA = 5sinA/sinA = 5
Believe me, I have seen that one done like that.
To find the value of (sin 5A)/(sin A), we can use a trigonometric identity called the Multiple Angle Identity:
sin nx = n(sin x)(cos^(n-1) x) - C(n) (sin^(n-2) x)(cos^2 x) for n > 1, where C(n) is the binomial coefficient.
In this case, we have n = 5 and x = A, so we substitute these values into the identity to get:
sin 5A = 5(sin A)(cos^4 A) - 10(sin^3 A)(cos^2 A)
Now, we substitute sin 5A into the expression (sin 5A)/(sin A):
(sin 5A)/(sin A) = [5(sin A)(cos^4 A) - 10(sin^3 A)(cos^2 A)] / (sin A)
We can simplify this expression by canceling out the common factor of sin A:
= 5(cos^4 A) - 10(sin^2 A)(cos^2 A)
By using another trigonometric identity, sin^2 A + cos^2 A = 1, we can rewrite the expression above as:
= 5(cos^4 A) - 10(1 - cos^2 A)(cos^2 A)
= 5(cos^4 A) - 10(cos^2 A - cos^4 A)
= 5(cos^4 A - cos^2 A) + 10(cos^4 A)
= 5cos^2 A(cos^2 A - 1) + 10cos^4 A
= -5cos^2 A + 10cos^4 A
Therefore, the value of (sin 5A)/(sin A) is -5cos^2 A + 10cos^4 A.