You are Here: Home >< Maths

# Further Maths question sin cos tan

Announcements Posted on
TSR's new app is coming! Sign up here to try it first >> 17-10-2016
1. (Original post by 1jonam16)
Basically, you need to write : LHS = 2tan squared theta + 1 first.
Then, what I normally do is write the two trigonometric identities, so tan theta = sin theta/cos theta and sin squared theta + cos squared theta =1.

Now, we know that tan theta is equal to sin theta/cos theta, therefore, use the same principle to get tan squared theta = sin squared theta/cos squared theta. However, as there's a 2 infront of the tan squared theta, you need ot double this like a normal fraction to get 2sin^2 theta / cos squared theta +....1 (this is the 1 that's left over - we haven't touched this).

Now you should have a fraction that looks like: (2Sin^2 Theta/Cos^2 Theta) + 1. Now we want to include the 1 in the whole fraction, so just do it like a normal fraction. Make the denominator of the 1 become cos^2 theta, by multiplying it by cos^2 theta. Hence, you end up witth (2sin^2 theta + cos^2 theta)/ cos ^2 theta.

Now if you rearrange the bottom of this, using sin^2 theta + cos ^2 theta = 1 (a trigonmetric identity), you know that cos ^2 theta = 1-sin^2 theta. Hence, you've got the denominator sorted.

Then, break up the numerator, to get sin ^2 theta + sin^2 theta + cos^2 theta INSTEAD of 2sin^2 theta + cos^2 theta. Now we know that sin^2 theta + cos ^2 theta =1. Therefore, the sin^2 theta + cos^2 becomes 1 , leaving you with 1 + sin^2 theta.

Now both parts should match the RHS so just say that.
Simples.
If this helped repping me would be appreciated, thanks.

Thank you so much! Sorry I seemed to have missed your post before. This has helped so much, we only started learning further maths a few weeks ago and the exam is tomorrow thanks again
2. Yep no worries, try to go thorugh it step by step. Btw do you know how to do q16, i.e. the bottom denomintor? I used the factor theorem and got the right answer, but the mark shceme does it differently, please could you explain how?
(Original post by jazz_xox_)
Thank you so much! Sorry I seemed to have missed your post before. This has helped so much, we only started learning further maths a few weeks ago and the exam is tomorrow thanks again
3. (Original post by 1jonam16)
Yep no worries, try to go thorugh it step by step. Btw do you know how to do q16, i.e. the bottom denomintor? I used the factor theorem and got the right answer, but the mark shceme does it differently, please could you explain how?
For the bottom denominator, I just factorised normally to get (x^2 - 1)(x^2 - 4)

I then re-factorised each bracket to be the difference of 2 squares to get:
(x + 1)(x - 1) and (x + 2)(x - 2)

I then cancelled the (x + 1) with the one on the numerator, and the same for the (x - 2)

which leaves you with
x^2 / (x - 1)(x + 2)

Hope this makes sense. Are you sitting the exam tomorrow?
4. Yeh i am, and i just realised you can simply break the bottom up. Okay thanks, I'm so stupid lol, wish i had seen that.
(Original post by jazz_xox_)
For the bottom denominator, I just factorised normally to get (x^2 - 1)(x^2 - 4)

I then re-factorised each bracket to be the difference of 2 squares to get:
(x + 1)(x - 1) and (x + 2)(x - 2)

I then cancelled the (x + 1) with the one on the numerator, and the same for the (x - 2)

which leaves you with
x^2 / (x - 1)(x + 2)

Hope this makes sense. Are you sitting the exam tomorrow?
5. (Original post by 1jonam16)
Yeh i am, and i just realised you can simply break the bottom up. Okay thanks, I'm so stupid lol, wish i had seen that.
It took me a while.. I'm so nervous for tomorrow's exam these past papers are hurting my brain

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: June 19, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### How does exam reform affect you?

From GCSE to A level, it's all changing

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams