I'm looking for some help on two questions, I think I have the first one but would like confirmation that I'm correct. The second one I'm getting slightly confused with.
Solve the following for 0 <= x <= pi
(i) Sin 5x - sin 2x = 0
(ii) Cos 5x + Sin 5x + Cos 3x + Sin 3x = 0
I use the sum and difference identities and get:
2cos (7x/2) * sin (3x/2) = 0
Therefore when either of these equal zero the statement is true.
2cos (7x/2) = 0
x = pi/2 as a general solution and calculate the next six.
the divide by 7/2 to give x and select the ones in the correct range which are:
pi/7, 3pi/7, 5pi/7 & pi
Do the same for Sine (3x/2) = 0 and I get 0 & 2pi/3.
These are all the solutions.
Is this correct??
(ii) It looks like this is a case of two sum and difference identities combined but I just get into a mess.
Can anyone help???