Math Is Fun Forum

Fla$h

Member

Registered: 2009-08-15

Posts: 10

Trigonometry Proofs

Hi Guys,i hope im posting in the right forum.Here Are A Few Exercises:-

PROVE THE FOLLOWING:-

1)

2)

3)

4)

5)

6)

I got these out of a maths textbook

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Trigonometry Proofs

Hi Fla$h;

For #1)

Cross multiply and we have.

Last edited by bobbym (2009-08-15 20:04:19)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

juriguen

Member

Registered: 2009-07-05

Posts: 59

Re: Trigonometry Proofs

Hi!

I think I got the first one:

1.

Jose

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“Make everything as simple as possible, but not simpler.” -- Albert Einstein

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Trigonometry Proofs

Most trig proofs involve converting 'tan' and 'cot' to 'sin' and 'cos', and lots of fractions!

yamini

Member

Registered: 2009-08-10

Posts: 2

Re: Trigonometry Proofs

hey i got ans for 4th ques
;):)
sinA-2sincubeA/2coscubeA-cosA
take sinA common in numerator and cos A in denominator
we get
sinA(1-2sinsquareA)/cosA(2cossquareA-1)
cos2A formula is 1-2sinsquareA and 2cossquareA-1
so they both will get cancelled
we get
sinA/cosA=tanA
hence proved. :P:P:

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Trigonometry Proofs

Hi Fla$h;
Here is another way for #4

Last edited by bobbym (2009-08-16 10:26:21)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Trigonometry Proofs

Hi Fla$h;
for #6

Expand the LHS.

Last edited by bobbym (2009-08-16 12:56:20)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Fruityloop

Member

Registered: 2009-05-18

Posts: 143

Re: Trigonometry Proofs

Hi Fla$h!;
Here's #2...

using

we get

Last edited by Fruityloop (2009-08-21 12:11:56)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Trigonometry Proofs

Hi Fla$h;

Problem  #3 is not an identity.
It should read:

Now here is the proof for #3:

Now cross multiply:

Now substitute cos²(A) = 1- sin²(A) and clean up:

Last edited by bobbym (2009-08-21 16:12:07)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Trigonometry Proofs

Hi Fla$h;

For problem #5

Expanding the LHS and remembering that:

We get:

Now using:

and

We get:

Using:

Last edited by bobbym (2009-08-21 19:48:56)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.