Verify the identity csc x sec xcsc x sec x 1 tan x1 tan

Verify the identity. csc x - sec x/csc x + sec x = 1 - tan x/1 + tan x To verify the identify, start with the4 more complicated side and transform it to lock like the other side. Choose the correct transformations and transform the expression at each step. csc x - sec x/csc x + sec x = (Do not simplify.) = (Do not simplify.) 1 - tan x/1 + tan x

Solution

LHS

(csc x - sec x)/(csc x + sec x) = (1/sin x - 1/cos x)/(1/sin x + 1/cos x)

= (cos x - sin x)/(cos x + sin x) = (1 - tanx)/(1 + tanx) = RHS