Essential Questions Help!

[Jordan23]

Hey these are just some questions from the Essential textbook that I am struggling with, hopping somebody would be able to show me how to work them out!

3A Q16
If x=sec(theta)-tan(theta), prove that x+1/x=2sec(theta) and also find a simple expression for x-1/x in terms of theta.

And by the way are there any tricks or hints on how to start proofs like the one above?

3B Q1c
Expand tan(x+(y+z))

2E Q20b,c,d
See essential book

Thanks

[TrueTears]

Hi welcome to VN 

3B Q1c

try using addition compound angle formula



now use the same formula to simplify tan(y+z) and sub it back in

[Jordan23]

That's how I went about it but it just became really messy and was unable to simplify it to the correct answer.

[TrueTears]

Correct, it does get a bit messy, check your work, start again from subbing the value of tan(y+z) and slowly work each step.

If you still can't get it, I will post it up.

[Jordan23]

Yer got Q1c - Expanded incorrectly grouped (1-tan(x))*(tan(y)+tan(z)) when the first part wasn't in fact in brackets 1-tan(x)(tan(y)+tan(z)). So many tan(..) everywhere makes it look so confusing. Thanks True Tears, I always make those silly mistakes!

[TrueTears]

hah, happens to me, whenever i make silly mistakes and can not find where i made it, i just start from the beginning 

[Jordan23]

Help with the other 2 questions would be much appreciated, sorry unable to post diagram and question for Exercise 2E Q20b,c,d

[TrueTears]

a) Let the point where EC and FD meet be called X

Let and and where is a constant

now

and

but



so

equating a and b yields

b)

[TrueTears]

c)



but (since ie cancel out)







rectangle

[TrueTears]

3A Q 16

let





now , as required.

[Jordan23]

Thanks alot True Tears I normally leave the trig reciprocals in the form of cot and cosec etc but I see it's probably much easier with these types of questions to write them as 1/sin etc. Much easier to see how to go about it