C2 trig identities question

OP

Original post by m4ths/maths247

Wy has it become an equation?

I thought you had to do that to solve for x

Reply 3

Original post by mica-lwe

I'm stuck on this question:

Prove that, for all values of x, the value of the expression

(3sinx + cosx)^2 + (sinx - 3cosx)^2

is an integer and state its value.

I multiplied the brackets and collected terms and then canceled and I got
sinx^2 + cosx^2 = 0, from my notes I know this equals one but whatever way i try to find x I just get 0 = 0, help please?!

Do you mean

\sin ^2x + \cos ^2x

And where did the rest go

And what do you mean it =0, it doesn't

Reply 4

Original post by mica-lwe

I thought you had to do that to solve for x

You have an expression

It cannot suddenly become an equation

You are not solving anything for x

Reply 5

OP

Original post by TenOfThem

You have an expression

It cannot suddenly become an equation

You are not solving anything for x

how do you find the value of x without solving it though?

Reply 6

DestinySky

(3sinx + cosx)^2 + (sinx - 3cosx)^2

= 9sin^2 + 6sinxcosx + cos^2x + sin^2x - 6sinxcosx +9cos^2x
= 10sin^2x + 10cos^2x
= 10 (sin^2x + cos^2x)
= 10 (1)
=10

I think that's how you do it :smile:

Reply 7

Original post by mica-lwe

how do you find the value of x without solving it though?

You cannot solve anything since you do not have an equation

You are not trying to find a value for x

Read the question

Reply 8

Original post by DestinySky

**£&^&!@%*£

Please do not give full solutions

The forum guidelines are clear

http://www.thestudentroom.co.uk/showthread.php?t=403989

Reply 9

OP

Original post by DestinySky

(3sinx + cosx)^2 + (sinx - 3cosx)^2

= 9sin^2 + 6sinxcosx + cos^2x + sin^2x - 6sinxcosx +9cos^2x
= 10sin^2x + 10cos^2x
= 10 (sin^2x + cos^2x)
= 10 (1)
=10

I think that's how you do it :smile:

Thankyou! that makes sense to me, I divided by 10 instead of taking a factor of 10 out so thats where i went wrong

Reply 10

DestinySky

No problem :smile:

Glad I can help.

Reply 11

Original post by mica-lwe

Thankyou! that makes sense to me, I divided by 10 instead of taking a factor of 10 out so thats where i went wrong

I do not want to be rude

But you went wrong when you tried to "solve"

You completely misunderstood the nature of the question

A confusion between expression and equation is a serious confusion - do you actually understand where you went wrong

Reply 12

OP

Original post by TenOfThem

I do not want to be rude

But you went wrong when you tried to "solve"

You completely misunderstood the nature of the question

A confusion between expression and equation is a serious confusion - do you actually understand where you went wrong

I do i just completely forgot how to do these questions and that was the only way I could think of doing them, I haven't looked at them for a while so that will be why. But I do understand where I went wrong

Reply 13