Trig identities - Math Central

HOME

Math Central

Quandaries & Queries

Question from Michael, a student:

Well i read that i can only send ONE at a time, but these are small ones related to the same subject.

i hope you guys wont mind. This was an assignment that i had alot of difficulties on.

1) Determine if the following is an identity. If it is, prove it, If it isn't state it.

tan x + cot x = sec x * csc x

and

1 - (cos^2) x = 1+ (cot^2) x

Thanks very much and a happy new year

PS: this is grade 11 AP math xD

Michael,

General "big hammer" approach to prove something is a trig identity, assuming it only involves trig functions of x,2x,3x...

Put all tans cots, secs and cscs in terms of sine and cosine.
If necessary, use multiple-angle formulae to put sin nx and cos nx in terms of sin x and cos x.
use algebra to finish.

General approach to proving something is NOT a trig identity: find one value of x for which it is not true. Of course, a really cunning problem-setter can find non-identities that are true for 0,30,45,60,and 90 degrees but not in between!

Good hunting!
RD

Michael,

I want to add something to Robert's list.

If necessary use sin²(x) + cos²(x) = 1 and its many variants. By variants I mean for example if you want a similar expression with tan²(x) then since tan(x) = sin(x)/cos(x) divide both sides of sin²(x) + cos²(x) = 1 by cos²(x) to get tan²(x) + 1 = sec²(x).

Harley

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.