need an advice, please help?

Question

what is the easy way or technique in proving trigonometric identities?
ex. 1-cos/1-sin=tan

Answer 1

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

now use definitions of sin = opposite/hypotenuse
and cos = adjacent/hypotenuse to get

a/h -a^2/h^2 = o/h -o^2/h^2
ah - a^2 = oh - o^2 (after mulitplying equation by h^2)

we know from the pythagorean theorem that a^2 + o^2 = h^2
and we know that h = sqrt(a^2 + o^2)

therefore our next step is:
a*sqrt(a^2 + o^2) - a^2 = o*sqrt(a^2 + o^2) - o^2
a*sqrt(a^2 + o^2) - o*sqrt(a^2 + o^2) = a^2 - o^2

after squaring both sides we get:
a^2(a^2+o^2)+o^2(a^2+o^2)-2ao(a^2+o^2) =
a^4-2a^2o^2+o^2

a^4 + 2a^2o^2 - 2a^3o - 2ao^3 + o^4 = a^4 - 2a^2o^2 +o^4
2a^2o^2 - 2a^3o - 2ao^3 = - 2a^2o^2
4a^2o^2 = 2a^3o + 2ao^3
2ao = a^2 + o^2

now assume a = 3 and o = 5
2*3*5 = 30 and 3^2 + 5^2 = 34

therefore 2ao DOES NOT EQUAL a^2 + o^2

this proves that (1-cos)/(1-sin) DOES NOT EQUAL tan.

Answer 2

by working towards one of the known identities. replaceing a tan by sin/.cos also helps.

Answer 3

remember all the important identitites: double angle identities, half angle identitites, pythagoras identities.. most of the questions containing tan(theta) can be easily proven if you convert it to sin(theta)/cos(theta). the rest is done only by remembering the basic identites. and practice wil help you alot too.

Answer 4

This is incorrect. How can anyone prove what is not correct?

Answer 5

just memorize the formulas,so you won't have problems.