Determine the value of sum tan pi/4+sin a=?

### 1 Answer | Add Yours

For the beginning, we'll substitute the function tan pi/4 by it's value 1.

We'll transform the sum into a product. For this reason, we'll have to express the value 1 as being the function sine of an angle, so that the terms of the sum to be 2 matching trigonometric functions.

1 = sin pi/2

sin a + 1 = sin a + sin pi/2

sin a + sin pi/2 = 2sin [(a+pi/2)/2]*cos[ (a-pi/2)/2]

sin a + sin pi/2 = 2 sin [(a/2 + pi/4)]*cos[ (a/2 - pi/4)]

sin [(a/2 + pi/4)] = sin (a/2)*cos pi/4 + sin (pi/4)*cos (a/2)

sin [(a/2 + pi/4)] = (sqrt2/2)*[sin(a/2) + cos(a/2)]

cos[ (a/2 - pi/4)] = (sqrt2/2)*[sin(a/2) + cos(a/2)]

sin a + sin pi/2 = 2*(2/4)[sin(a/2) + cos(a/2)]^2

sin a + sin pi/2 = [sin(a/2) + cos(a/2)]^2

**tan pi/4+sin a = [sin(a/2) + cos(a/2)]^2**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes