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Trigonometric Identities 
(Math  Trig  Identities) 
sin(theta) = a / c  csc(theta) = 1 / sin(theta) = c / a 
cos(theta) = b / c  sec(theta) = 1 / cos(theta) = c / b 
tan(theta) = sin(theta) / cos(theta) = a / b  cot(theta) = 1/ tan(theta) = b / a 
sin(x) = sin(x)
csc(x) = csc(x)
cos(x) = cos(x)
sec(x) = sec(x)
tan(x) = tan(x)
cot(x) = cot(x)
sin^2(x) + cos^2(x) = 1  tan^2(x) + 1 = sec^2(x)  cot^2(x) + 1 = csc^2(x)  
sin(x y) = sin x cos y cos x sin y  
cos(x y) = cos x cosy sin x sin y 
tan(x y) = (tan x tan y) / (1 tan x tan y)
sin(2x) = 2 sin x cos x
cos(2x) = cos^2(x)  sin^2(x) = 2 cos^2(x)  1 = 1  2 sin^2(x)
tan(2x) = 2 tan(x) / (1  tan^2(x))
sin^2(x) = 1/2  1/2 cos(2x)
cos^2(x) = 1/2 + 1/2 cos(2x)
sin x  sin y = 2 sin( (x  y)/2 ) cos( (x + y)/2 )
cos x  cos y = 2 sin( (x  y)/2 ) sin( (x + y)/2 )
angle  0  30  45  60  90 

sin^2(a)  0/4  1/4  2/4  3/4  4/4 
cos^2(a)  4/4  3/4  2/4  1/4  0/4 
tan^2(a)  0/4  1/3  2/2  3/1  4/0 
Given Triangle abc, with angles A,B,C; a is opposite to A, b opposite B, c opposite C:
a/sin(A) = b/sin(B) = c/sin(C) (Law of Sines)

(Law of Cosines) 
(a  b)/(a + b) = tan [(AB)/2] / tan [(A+B)/2] (Law of Tangents)
cos(2x) = cos^2(x)  sin^2(x) = 2 cos^2(x)  1 = 1  2 sin^2(x)
In other words we can “factor” a multiplicative constant out of a limit.
thanx, and plz upload answer of 4th question
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