Math Is Fun Forum

user2011

Member

Registered: 2011-11-28

Posts: 2

Trig Proofs

Stumped on a couple trig identity proofs. A step-by-step would be greatly appreciated!

(1-(sin x - cos x)^2) / sin x = 2cos x

((1+cos x) / (sin x)) + ((sin x / 1+ cos x)) = 2csc x

Thanks!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Trig Proofs

hi user2011,

Here's a start which will hopefully be enough for you to fill the gaps.  (But you may post back for more help if gaps are  too big.)

(1)

Clear bracket and simplify by using

You should be left with just one term on the top, cancel the sin and you get the RHS.

(2)

Now use the same trig identity as in (1) to simplify the top, factorise and cancel a common factor top and bottom.

What's left is the RHS.

Hope that helps. 

Bob

Last edited by Bob (2011-11-28 09:30:25)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

user2011

Member

Registered: 2011-11-28

Posts: 2

Re: Trig Proofs

thanks!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Trig Proofs

You're welcome.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob