I don't even know where to start. :(
a) (sin10x)/(sin9x +sinx) = (cos5x)/(cos4x).
b) (sinx)/(sin x/2) - (cosx)/(cos x/2) = (sec x/2)
I can only use the following identities:
Reciprocal, Pythagorean, sum and difference, double-angle, power reducing, half-angle, sum-to-product, and product-to-sum.
You can only work one side at a time. You cannot manipulate both sides.
Please tell me what to do step by step (at least list the formulas you used in order, etc.).
a) (sin10x)/(sin9x +sinx) = (cos5x)/(cos4x).
b) (sinx)/(sin x/2) - (cosx)/(cos x/2) = (sec x/2)
I can only use the following identities:
Reciprocal, Pythagorean, sum and difference, double-angle, power reducing, half-angle, sum-to-product, and product-to-sum.
You can only work one side at a time. You cannot manipulate both sides.
Please tell me what to do step by step (at least list the formulas you used in order, etc.).
-
a)
(sin10x)/(sin9x + sinx) = 2sin5xcos5x (double-angle)/(sin9x + sinx)
2sin5xcos5x / 2sin[(9x + x)/2]cos[(9x - x)/2] (sum to product)
2sin5xcos5x / 2sin5xcos4x
cos5x/cos4x
(sin10x)/(sin9x + sinx) = 2sin5xcos5x (double-angle)/(sin9x + sinx)
2sin5xcos5x / 2sin[(9x + x)/2]cos[(9x - x)/2] (sum to product)
2sin5xcos5x / 2sin5xcos4x
cos5x/cos4x