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1. Using the identity cos(A+B)= cosAcosB - sinAsinB, prove that

cos2A = 1-2sin^2 A

So far I've got that cos2A = cos^2 A - sin^2 A

but I dont know where to go from here.. any help?
2. (Original post by JosephinaMarley)

Using the identity cos(A+B)= cosAcosB - sinAsinB, prove that

cos2A = 1-2sin^2 A

So far I've got that cos2A = cos^2 A - sin^2 A

but I dont know where to go from here.. any help?
Use the identity sin^2 A + cos^2 A = 1
3. (Original post by Clarity Incognito)
Use the identity sin^2 A + cos^2 A = 1
But its not '+', all I have is a minus...
4. (Original post by JosephinaMarley)

Using the identity cos(A+B)= cosAcosB - sinAsinB, prove that

cos2A = 1-2sin^2 A

So far I've got that cos2A = cos^2 A - sin^2 A

but I dont know where to go from here.. any help?

say b=A

cos(A+A)=cosAcosA-sinASinA

Cos2A=(cosA)^2-(sinA)^2

we want sin only so substitue in 1-sin^2A=(cosA)^2

cos2a=1-sin^2A-sin^2A=1-2sin^2A
5. (Original post by JosephinaMarley)
But its not '+', all I have is a minus...
Rearrange and substitute then!
6. Cos2A = Cos^2A - Sin^2A
=2cos^2A - 1
=1-2sin^2A
7. cos (A+B) = cosAcosB - sinAsinB
so
cos (A+A) = cosAcosA - sinAsinA
cos (2A) = cos^2 A - sin^2 A
cos 2A = cos^2 A - (1-cos^2 A) *(using sin^2 A + cos^2 A = 1)
cos 2A = cos^2 A -1 + cos^2 A
cos 2A = 2cos^2 A -1

Hope this helped...
8. (Original post by Remarqable M)
say b=A

cos(A+A)=cosAcosA-sinASinA

Cos2A=(cosA)^2-(sinA)^2

we want sin only so substitue in 1-sin^2A=(cosA)^2

cos2a=1-sin^2A-sin^2A=1-2sin^2A
Thankyou!!! I feel so dull for not seeing that!
9. Ryt, here goes.myt be a bit l8 considering the exam is in 2 hours

Cos^2 A - Sin^2 A= Cos^2 A -(1- Cos^2 A)

= 2Cos^2 A -1= 2(1-Sin^2 A)-1

= 2-2Sin^2 A -1

=1-2Sin^2 A

Boom!

ur welcome

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