You are Here: Home >< Maths

# C3 Trig Identity watch

1. There is a question which says
"Prove cot 1/2A - tan 1/2A is identical to 2 cotA"
Have been trying to solve it and it's gotten me nowhere.

I've tried multiplying everything by tan but that gave me the wrong answer.
2. (Original post by B_Kazi)
There is a question which says
"Prove cot 1/2A - tan 1/2A is identical to 2 cotA"
Have been trying to solve it and it's gotten me nowhere.

I've tried multiplying everything by tan but that gave me the wrong answer.
use the substitution t=tan1/2a and the formula tan(2a)= 2tana/1-tan^2a
3. First merge them, changing them to their sine and cosine versions so youll get (cosA/2 squared - sinA/2 squared)/(sinA/2 x cosA/2)

Now the important part
cos2A = cosA squared - sinA squared
so, cosA = cosA/2 squared - sinA/2 squared (just divide all angles of the original double angle formula by 2)

now we have the numerator fixed, so for the denominator

sin2A = 2sinAcosA
similarly, sinA =2sinA/2 x cosA/2
divide the above equation by 2 to get sinA/2 x cosA/2 , which is (sinA)/2. or lets call it 0.5sinA

thats the denominator

Now, when we replace the numerator and denominator we have (cosA) / .5sinA
cosA/sinA = cotA, diving that by .5 is same as multiplying it by 2 (since division essentially means multiplying with recriprocal)
4. late again ...
5. (Original post by N92991)
First merge them, changing them to their sine and cosine versions so youll get (cosA/2 squared - sinA/2 squared)/(sinA/2 x cosA/2)

Now the important part
cos2A = cosA squared - sinA squared
so, cosA = cosA/2 squared - sinA/2 squared (just divide all angles of the original double angle formula by 2)

now we have the numerator fixed, so for the denominator

sin2A = 2sinAcosA
similarly, sinA =2sinA/2 x cosA/2
divide the above equation by 2 to get sinA/2 x cosA/2 , which is (sinA)/2. or lets call it 0.5sinA

thats the denominator

Now, when we replace the numerator and denominator we have (cosA) / .5sinA
cosA/sinA = cotA, diving that by .5 is same as multiplying it by 2 (since division essentially means multiplying with recriprocal)
I would recommend using a different letter for your standard identities, rather than jumping from A and A/2 to 2A and A.

### 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: March 9, 2016
Today on TSR

### He broke up with me because of long distance

Now I'm moving to his city

### University open days

1. Norwich University of the Arts
Thu, 19 Jul '18
2. University of Sunderland
Thu, 19 Jul '18
3. Plymouth College of Art
Thu, 19 Jul '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