Here we have to prove secq(1-sinq)(secq + tanq) = 1 we will start with LHS (Left hand side ie secq(1-sinq)(secq + tanq) ) and prove that it is equal to 1 Hence we will get LHS = RHS
Our aim is to Show that secq(1-sinq)(secq + tanq) = 1
Proof
Lets start with LHS of the equations
LHS = secq(1-sinq) (secq + tanq)
= (secq-sinq×secq) (secq+tanq)
= (secq-tanq) (secq+tanq) hint : secq=1/cosq and sinq/cosq=tanq
= (sec²q-tan²q) hint : (x+y)(x-y)=x²-y²
= 1 hint : we know sec²q-tan²q =1
= RHS
Hence proved RHS = LHS ie secq(1-sinq)(secq + tanq) = 1