I need help with proving trigonometric identities!
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I need help with proving trigonometric identities!

[From: ] [author: ] [Date: 11-05-27] [Hit: ]
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.).......
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) = 2sin5xcos5x (double-angle)/(sin9x + sinx)

2sin5xcos5x / 2sin[(9x + x)/2]cos[(9x - x)/2] (sum to product)

2sin5xcos5x / 2sin5xcos4x

cos5x/cos4x
1
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