# Trig problems giving a hard time.

1. Jul 24, 2013

### labin.ojha

I was having some free time and decided to do some mathematics from my high school mathematics book.These two problems remained, and I am completely clueless to the solution approach.

1. The problem statement, all variables and given/known data

A. If sin(θ)-cos(θ)=1, prove that sin(θ)+cos(θ)=±1
B. If tan(θ)+sec(θ)=10, prove that sin$^{2}$(θ)+cos$^{2}$(θ)=1

2. Relevant equations

3. The attempt at a solution

The approach to both problems were similar, I squared both sides of the given equations, and used trig identities at an attempt of simplifying.

That got me nowhere.

Last edited: Jul 24, 2013
2. Jul 24, 2013

### haruspex

That certainly works for A. If you still can't see it, please post your working.
For B, pay close attention to what is to be proved.

3. Jul 24, 2013

### labin.ojha

Found a way for A:

sin(θ)-cos(θ)=1
[Squaring]
sin$^{2}$(θ)-2sin(θ)cos(θ)+cos$^{2}$(θ)=1=sin$^{2}$(θ)+cos$^{2}$(θ)
sin$^{2}$(θ)+cos$^{2}$(θ)=sin$^{2}$(θ)+2sin(θ)cos(θ)+cos$^{2}$(θ)
1=(sin(θ)+cos(θ))$^{2}$
[Taking square roots]
sin(θ)+cos(θ)=$\pm$1

For B, the 'to prove' equation is an identity but getting it from the given expression is being a problem
because as I square the both sides , it gets messier and hopeless.

Last edited: Jul 24, 2013
4. Jul 24, 2013

### Dick

If the equation to be proved is an identity, you don't have to get it from the other expression. It's just plain always true.

5. Jul 24, 2013

### labin.ojha

Yes, it is. But I'll look for the solution and post it here as soon as i get it .

EDIT:
the question seems to have been removed from the new edition of the book, mine was an old one.

Last edited: Jul 24, 2013
6. Jul 24, 2013

### Dick

There's really nothing to look for or get. This is exactly like proving "If x=2 then x=x." x=x is true regardless of whether x=2 is true. So "If x=2 then x=x." is a true statement.

7. Jul 24, 2013

### Dick

Removing it is a good idea. In the context of proving trig stuff, it's only going to cause confusion.

8. Jul 24, 2013