# Please help me with this problem

Tags:
1. Mar 24, 2016

### vijayramakrishnan

1. The problem statement, all variables and given/known data
cos(θ)^x+sin(θ)^x=1
find the number of real values of x satisfying this equation

2. Relevant equations
none

3. The attempt at a solution
the answer given is 1 which is 2.which is obvious but i don't know how to prove that it is the only solution available

Last edited by a moderator: Mar 25, 2016
2. Mar 25, 2016

### Nathanael

You want to prove there is no x, other than 2, which gives equality for all values of θ.

Choose any particular θ and show that the only x-value for that particular θ which gives equality is x=2 (that would prove it, right?)

What particular value of θ might it be easy to show this for?

3. Mar 25, 2016

### vijayramakrishnan

thank you for replying sir,i want to prove that 2 is the only solution possible.

4. Mar 25, 2016

### Nathanael

When you say "the only solution possible," what you really mean is, "the only solution possible for all values of θ" right?

If you were to choose a particular value of θ and prove that 2 is the only solution for that θ, then that would prove what you want, because if x is not 2 then x does not solve it for that particular θ you chose.
This means you only have to prove it for any single value of θ. Do you agree?

I didn't want to hint at it too much, but if you choose the θ such that cosθ=sinθ then you can factor together the exponent x and complete the proof.

5. Mar 25, 2016

### vijayramakrishnan

thank you sir, from there i will try on my own

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted