cscx-sinx=(cosx)(cotx)
1/sinx-sinx=(cosx)(cosx/sinx)
(1/sinx)-(sin^2x/sinx)=cos^2x/sinx
cos^2x/sinx=cos^2x/sinx
Therefore LS=RS
You have to remember some trig identities when answering these questions. In this case, you need to recall that sin^2x+cos^2x=1. Also, always switch tanx cotx cscx secx in terms of sinx and cosx.
Chat with our AI personalities
Suppose csc(x)*sin(x) = cos(x)*cot(x) + y then, ince csc(x) = 1/sin(x), and cot(x) = cos(x)/sin(x), 1 = cos(x)*cos(x)/sin(x) + y so y = 1 - cos2(x)/sin(x) = 1 - [1 - sin2(x)]/sin(x) = [sin2(x) + sin(x) - 1]/sin(x)
cot x = (cos x) / (sin x) cos (x - 180) = cos x cos 180 + sin x sin 180 = - cos x sin (x - 180) = sin x cos 180 - cos x sin 180 = - sin x cot (x - 180) = (cos (x - 180)) / (sin (x - 180)) = (- cos x) / (- sin x) = (cos x) / (sin x) = cot x
cosec(q)*cot(q)*cos(q) = 1/sin(q)*cot(q)*cos(q) = cot2(q)
Cot x is 1/tan x or cos x / sin x or +- sqrt cosec^2 x -1
the questions is 2x=(cot^2 x-1)/(cot^2 x+1)