Help urgent integration

Alevelhelp.1

Help! How do I get this I don’t understand I got

Sin^2 2x = 1/2 - 1/2cos4x
But that’s wrong

(edited 10 months ago)

Reply 1

Marvel_fan

Hi! They're using the identity sin^2(x) + cos^2(x) = 1 in that first line
Does that help you figure out the next steps?

Reply 2

Alevelhelp.1

Original post by Marvel_fan

Hi! They're using the identity sin^2(x) + cos^2(x) = 1 in that first line
Does that help you figure out the next steps?

I don’t get it 😭
what are they subbing that identity in for??

Reply 3

Pxnyl_

Original post by Alevelhelp.1

I don’t get it 😭
what are they subbing that identity in for??

They haven't subbed it in but they used that identity and rearranged it to give cos^2(2x) = 1-sin^2(2x)

(edited 10 months ago)

Reply 4

davros

Original post by Alevelhelp.1

Help! How do I get this I don’t understand I got

Sin^2 2x = 1/2 - 1/2cos4x
But that’s wrong

They're just using trig identities to simplify things as much as possible before integrating.

First they use 1-sin^2A = cos^2A which should be imprinted on your brain by now :smile:

Then they use sinA/cosA = tan A and the "spare" 1/cosA becomes secA. This leaves you with something of the form secAtanA which you should recognise as a standard integral - it's probably in your formula book :smile: