Verify if sin25+sin35=cos5
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We have to verify sin 25 + sin 35 = cos 5
sin 25 + sin 35
=> 2* sin (25 + 35)/2 * cos 10/2
=> 2* sin (60)/2 * cos 5
=> 2* sin 30 * cos 5
sin 30 = 1/2
=> 2 * (1/2) cos 5
=> cos 5
This proves that sin 25 + sin 35 = cos 5
Supposing that 25,35 and 5 are degrees, we'll transform the sum of matching trigonometric functions into a product.
We'll use the formula:
sin a + sin b = 2sin [(a+b)/2]*cos[(a-b)/2]
According to this formula, we'll obtain:
sin 25 + sin 35 = 2sin [(25+35)/2]*cos[(25-35)/2]
sin 25 + sin 35 = 2sin [(60)/2]*cos[(-10)/2]
sin 25 + sin 35 = 2sin 30*cos(-5)
Since the cosine function is even, we'll get:
sin 25 + sin 35 = 2sin 30*cos(5)
But sin 30 = 1/2
sin 25 + sin 35 = (2/2)*cos(5)
sin 25 + sin 35 = cos 5
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