Question

cos(x/5) sin(x/5)=½[sin(2x/5)]
true or false?

Answer 1

are you familiar with the identity sin(2a) = 2sinacosa?

Answer 2

let's make it prettier

sin(2a) = 2sin(a)cos(a)

Answer 3

Im not familiar with it.

Answer 4

well your teacher should teach that to you before giving these exercises lol =)) anyway keep that in mind coz im going to use that here and it is used a lot in later maths

sin(2a) = 2sin(a)cos(a)

now if i replace a by x/5 i will get

sin (2x/5) = 2sin(x/5)cos(x/5)

agree?

Answer 5

okay yeah

Answer 6

now if i divide both sides by 2 i will get

\[\large \frac{\sin (\frac{2x}{5})}{2} = \sin (\frac{x}{5}) \cos (\frac{x}{5})\] ^the 2 in the right side got canceled

Answer 7

now what can you conclude?

Answer 8

That its false?

Answer 9

let me rewrite that...i can express this as \[\frac{1}{2} \sin (\frac{2x}{5}) = \sin (\frac{x}{5}) \cos (\frac{x}{5})\]

Answer 10

isn't \[\frac{a}{2} = \frac{1}{2} a?\]

Answer 11

now again..is the equation in your question true? or false?

Answer 12

The last one makes sense. True.

Answer 13

there you go :D

Answer 14

thanks (: