Expert Answers
justaguide eNotes educator| Certified Educator

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

giorgiana1976 | Student

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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