prove the following identities?

Question

prove the following identities: i need major help asap!!

A) tan0cot0=1
B) tanA/secA=sinA
C) cotA/cscA=cosA
D) sin x (sec x + csc x) = tan +1
E) 1-sin0=cos^20/1+sin0

Answer 1

You will mostly want to know your basic definitions of the reciprocal functions: cot = 1/tan, sec = 1/cos, and csc = 1/sin. With those several of the problems are almost immediate. For example, "A" becomes tan * 1/tan = tan / tan = 1. "B" and "C" are similar.

For "E", you need to know sin^2 + cos^2 = 1. Because of that property, cos^2 = 1 - sin^2. You can factor 1 - sin^2 into
(1 + sin)(1 - sin), so the right side is the same thing as
(1 + sin)(1 - sin)/1 + sin. You just cancel the factors of "1 + sin", and you've got the left side. "D" is similar, using the identity tan^2 + 1 = sec^2.

(I've left out the variables in all the trig expressions, but you would of course include them in your answers.)

Answer 2

confirm: cos x + sin x tan x = sec x Take the LHS. cos x + sin x tan x = remember that tan x = sin x / cos x. cos x + sin x (sin x / cos x) = cos x + (sin²x / cos x) = Multiply the 1st term by using (cos x / cos x) so as which you have a uncomplicated denominator for the two words. cos x(cos x / cos x) + (sin²x / cos x) = (cos²x / cos x) + (sin²x / cos x) = combine. (cos²x + sin²x) / cos x = remember cos²x + sin²x = a million a million / cos x = remember that sec x = a million / cos x. sec x = RHS