2010 Paper 1 Q2 - Trig functions & intregration

2.  (i) Show that (sin x + cos x)² = 1 + sin 2x.

     (ii) Hence find, in terms of π, the value of

(i) We need to remember our identities for this one. Whenever we are asked to “show”, we need to remember that we have to use either the left-hand side (LHS) and work our way to the right-hand side (RHS) of the equation, or vice versa.

In this case, we will start with the LHS.

Why LHS? Well, it is because the LHS will be able to provide us with more information to work with. Hence, whenever you need to prove, always choose the one that will be able to provide more information.

So here goes…

Taking the LHS,

(sin x + cos x)² = sin² x + 2sinxcosx + cos² x

                                = sin² x + cos² x + 2sinxcosx

                                = 1 + 2sinxcosx

                                = 1 + sin 2x

                                = RHS  (shown)