Question

since sin2A=2sinAcosA, what is sin1/2A?

Answer 1

isn't it just equals to sin1/2Acos1/2A?

Answer 2

Sin2a = 2sinAcosA

If we apply inverse sin to both sides of the equation:

2A = sin^-1(2sinAcosA)

sin1/2A
sin1/sin^-1(2sinAcosA)

Answer 3

why must we inverse both sides?

Answer 4

When you inverse both sides of the equation you make the angle (2a) by itself. This is necisary in solving sin1/2a. In the denominator 2a is by itself, and not the sin,

Answer 5

what is the ans for sin1/2A then?

Answer 6

It can only be solved in terms of variables; seeing is though it cannot be solved in any other methods.

Answer 7

sin1/2a = sin1/sin^-1(2sinAcosA)

Answer 8

actually i got this result,
sin2A=2sinAcosA
so i was thinking, can't we replace A with 1/2A to get sin1/2A? ie sin1/2A = 2sin1/2Acos1/2A

Answer 9

No, you cannot replace A with 1/2A.....
How can you replace A with 1/2A. They are different numbers

Answer 10

then how did this step come about? from
4sin1/2xcos1/2x
=2sinx
it's a solution from my math book

Answer 11

I don't know how your maths book achieved any answer. I don't know where the x came from either. The equation can only be simplified.

Answer 12

Or solved in terms of variables. This is what I have done

Answer 13

Is it sin A/2 or 1/(2A)?

Answer 14

the second one

Answer 15

U can write 1/2A = 1/4A + 1/4A and use double angle if u want...