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# trig questions c4

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1. The Q is, solve the equation, Tan2X = 3Tanx for 0 to 2 Pi (interval),

Right I changed Tan 2X into the double angle identity, and took 3Tanx to the other side, I thought since its equal to 0 the bottom part of the fraction, of the double angle identity will cancel out but it dosent in the answer?

Btw the identity for tan2x is 2TanX/ 1- Tanx^2
2. (Original post by SunDun111)
The Q is, solve the equation, Tan2X = 3Tanx for 0 to 2 Pi (interval),

Right I changed Tan 2X into the double angle identity, and took 3Tanx to the other side, I thought since its equal to 0 the bottom part of the fraction, of the double angle identity will cancel out but it dosent in the answer?

Btw the identity for tan2x is 2TanX/ 1- Tanx^2

The denominator does "cancel" out when you multiply through by the denominator, but that means you need to multiply th 3 tan x by the denominator too.

The reason why works is by multiplying by the denominator.

3. (Original post by Zacken)

The denominator does "cancel" out when you multiply through by the denominator, but that means you need to multiply th 3 tan x by the denominator too.

The reason why works is by multiplying by the denominator.

Yeah I figured it out that was the question and i got the answers, now im kinda stuck on another,

The question is 2 Cos x^2 = 2SinxCosx + 1

How can I do this? Do i need to factorise it so i can solve two equations?
4. Maybe this helps: 2sinxcosx+1=(sinx+cosx)^2
5. (Original post by SunDun111)
Yeah I figured it out that was the question and i got the answers, now im kinda stuck on another,

The question is 2 Cos x^2 = 2SinxCosx + 1

How can I do this? Do i need to factorise it so i can solve two equations?
Move the one over to the other side of the equation:

but this is precisely by using your trig identities.

Hence:
6. (Original post by Math12345)
Maybe this helps: 2sinxcosx+1=(sinx+cosx)^2
I can't immediately see how this is helpful?
7. (Original post by Zacken)
I can't immediately see how this is helpful?

or
or
Now solve.

8. (Original post by Math12345)

or
or
Now solve.

I see, bit long winded but it'd do. Thanks.

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