You are Here: Home >< Maths

# 1(ii) Explain why tan x > sin x for 0<x<90 watch

2. (Original post by shushmush)
Have you done part (i)?
3. Yes
4. (Original post by shushmush)
Yes
You know that since and for . Try factorising the expression and tell me what you think.
5. (Original post by shushmush)
Yes
Sorry, didn't see this as I wasn't quoted.

So because the interval is 0 < x < 90, you know that the RHS is always going to be positive as both sin(x) and tan(x) are both positive for this range, so sin2(x) and tan2(x) will be too.

6. (Original post by Protostar)
Sorry, didn't see this as I wasn't quoted.

So because the interval is 0 < x < 90, you know that the RHS is always going to be positive as both sin(x) and tan(x) are both positive for this range, so sin2(x) and tan2(x) will be too.

I'm not sure how to factorise the LHS.
7. (Original post by shushmush)
I'm not sure how to factorise the LHS.
Are you familiar with the difference of two squares?
8. Ohhhh I get the factorisation now
(Original post by Protostar)
Are you familiar with the difference of two squares?
9. (Original post by shushmush)
Ohhhh I get the factorisation now
Great so what do you spot?
10. (Original post by Protostar)
Great so what do you spot?
What am I meant to spot?
11. (Original post by shushmush)
What am I meant to spot?
We've established that the RHS is always positive for values of x in this range. Because of the identity, the LHS must also be positive. Look at the result of your factorisation, keeping this in mind, and things should become reasonably clear
12. (Original post by Protostar)
We've established that the RHS is always positive for values of x in this range. Because of the identity, the LHS must also be positive. Look at the result of your factorisation, keeping this in mind, and things should become reasonably clear
Thank you!
13. (Original post by shushmush)
Thank you!
No worries, hope that helped
14. tan x is sinx/cosx

cosx is between 0 and 1 not inclusive

if you divide by a positive number less than 1 your answer gets bigger.
15. (Original post by shushmush)
...
You've established that

We know that the RHS is for because it's a whole square term (anything squared is always +ve)

So, you essentially have for

We can simplify this by dividing by one of the expressions, but you need to reason WHY you're allowed to divide by one of them. Which would leave you with the other expression and the inequality, thus granting the result.
16. (Original post by RDKGames)
We know that the RHS is for because it's a whole square term (anything squared is always +ve)
Just a pedantic quibble on language but real numbers squared are always non-negative, not necessarily positive; you can get zero, and the fact that you don't in this case is important to the argument.
17. (Original post by I hate maths)
Just a pedantic quibble on language but anything squared is always non-negative, not necessarily positive; it can be zero, and the fact that it's not in this case is important to the argument.
For more pedantry: any real number squared is always non-negative; i^2 = -1.
18. (Original post by I hate maths)
Just a pedantic quibble on language but anything squared is always non-negative, not necessarily positive; it can be zero, and the fact that it's not in this case is important to the argument.
Yes anything (real) squared is non-negative, but in this context we have , so the product squared is strictly positive as I said.
19. (Original post by Zacken)
For more pedantry: any real number squared is always non-negative; i^2 = -1.
Ah yeah, edited it immediately after it went up but it seems it wasn't on time.

### Related university courses

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:
Updated: November 14, 2017
The home of Results and Clearing

### 3,827

people online now

### 1,567,000

students helped last year
Today on TSR

Hang on, have Edexcel's come out already?

### University open days

1. SAE Institute
Animation, Audio, Film, Games, Music, Business, Web Further education
Thu, 16 Aug '18
2. Bournemouth University
Fri, 17 Aug '18
3. University of Bolton
Fri, 17 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams