Give 20 examples of proving trigonometric identities?

Answer 1

There are truly hundreds of trig identities, and most are quite complex, and although direct, often times somewhat difficult to prove, especially online. There are many math websites maintained for this purpose: presenting common mathematical proofs. A simple google search should allow you to find this quite easily.

Answer 2

It is extremely difficult to type in the proof of trigo identities in the computer.
However, if you are a student you will have the text books and other resources that can provide you with many examples. of the proof.

If you want the method - then it is easier to tell you.... but 20 examples.... difficult.

Answer 3

i'm assuming you advise sin² x / ( a million - cos x) = a million + cos x Then using sin² x = a million - cos² x interior the left hand fringe of the above equation you get (a million - cos² x) / (a million - cos x) = a million + cos x Now, a million - cos² x is the version of two sq. numbers and so this aspects to (a million + cos x)(a million - cos x) substituting this into the above equation you get (a million + cos x)(a million - cos x) / (a million - cos x) = a million + cos x Now for cos x no longer = a million (i.e. no longer PI / 2) then a million - cos x might want to correctly be factored from the Left Hand fringe of the equation leaving a million + cos x = a million + cos x and that is your answer

Answer 4

To prove:
sin(x) = ( (e^ix) - (e^-ix) ) / 2i
where x is any real number and i^2 = -1


e^ix = 1 + ix + ((ix)^2)/2! + ((ix)^3)/3! + ((ix)^4)/4! ...
e^-ix = 1 + (-ix) + ((-ix)^2)/2! + ((-ix)^3)/3! + ((-ix)^4)/4! ...

use i^2 = -1 and i^4 = +1 and i^3 = -i

subtract e^-ix from e^ix (all the even powers cancel out, leaving only terms in 2*i)

divide by 2 i, leaving only terms in x, in the form :

x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ....

and you are done.

Easy, no?