Verify the identity sin2 tcos t sec t cos t To verify the

Verify the identity. sin^2 t/cos t = sec t - cos t To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression at each step. sin^2 t/cos t = /cos t = (Do not simplify.) = = sec t - cos t

Solution

sin² t / cos t = sec t - cos t

LHS: [ use identity sin²t + cos² t = 1]

sin² t / cos t = 1- cos² t / cos t

= (1/ cos t ) - ( cos² t/ cos t)

= sec t - cos t ( sec t = 1/ cos t)

= RHS

LHS = RHS