The common error in proving trigonometric identities is to assume the equality of the left-hand side (LHS) and the right-hand side (RHS) of what is being proved. To prove an identity means to transform the LHS and RHS in the same form.
Prove the identity:
Solution sure to get 0/5 mark:
This is a ratio so we cross multiply. That is,
Why you get 0 mark? When you cross-multiply, you assume that you have an equation. You assume that the left-hand side is equal to the right-hand side. Isn’t that’s what you are exactly asked to do – To show that they are equal and not assume that they are equal?
Solution sure to get 5/5 mark:
Left Hand Side
Right Hand Side
The right hand side is identical to the left hand side hence the identity is proved.