Question

cos t(sec t - cos t)

simplify the expression

Answer 1

Remember:
sec t=1/cos t
sin²t+cos²t=1            ⇒sin²t=1-cos² t

Therefore: 
cos t(sec t- cost)=(cos t* sec t)- cos² t=(cos t * 1/cos t)-cos² t=1-cos²t=sin² t

Answer: cos t(sec t-cos t)=sin² t