Help how do I get this answer maths

Alevelhelp.1

Help how do I get this from the double angle formula? I’m confused where does the 1/2 come from plz can someone help

(edited 10 months ago)

Reply 1

mqb2766

You know
sin(2A) = 2sin(A)cos(A)
So A = 3x and divide through the identity by 2.

Reply 2

Alevelhelp.1

Original post by mqb2766

You know
sin(2A) = 2sin(A)cos(A)
So A = 3x and divide through the identity by 2.

Ahh I see thank you, but I did this
I did sin (2x+x) as the identity and for it wrong :frown:

Reply 3

mqb2766

Youd have to post your working to see what you actually did, but a simple rule of thumb is if you see a product of two trig terms like
sin*cos or sin^2 or cos^2
then that corresponds to a double angle. Similarly a triple angle corresponds to a product of three trig terms ... Here you had an integation problem and its generally easier to integerate a single trig term (double/triple angle) than a product, though you could have noted here that cos is the derivative of sin, so either reverse chain or substitution with
u = sin(3x)
would work as well.

(edited 10 months ago)