Math Is Fun Forum

Borbarad

Member

Registered: 2009-05-09

Posts: 1

Trigonometric Identities (Sin/Cos- Proving how to do them)

Hi guys! Couple of quick questions-

1. (tan^2(x) +1) (cos^2(x) +1)= tan^2(x) +2

2. sin^3(x) - cos^3(x) divided by sin(x)-cos(x)= 1+sin(x)cos(x)

The basic idea is to prove that whatever is on the left side is exactly the same thing as the stuff on the right side... so.. (in the end) i should get 1+sin(x)cos(x)=1+sin(x)cos(x). Im confused on how to get to that point however.

Thanks a ton for all the help!

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Trigonometric Identities (Sin/Cos- Proving how to do them)

For 1), expand the brackets. There will be a tan²(x)cos²(x) term in the expansion, which can be changed into something simpler. From there it's easy to get to the finish.

For 2), I'd take the denominator over to the RHS, then expand that and manipulate it until you get sin³(x) - cos³(x).

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Why did the vector cross the road?
It wanted to be normal.

nurshodiq

Member

Registered: 2009-03-29

Posts: 12

Re: Trigonometric Identities (Sin/Cos- Proving how to do them)

#2. we have algebra formula :

then

Last edited by nurshodiq (2009-05-10 00:09:42)