## Proving Trigonometrical Identities (A level)

Proving trigonometrical identities requires you to use mathematical and logical steps to prove that one side of the identity can be simplified into the other side of the equation. Logically you cannot work from both sides of the identity at the same time.

Since we will be simplifying one side to prove that it is equal to the other side, it is helpful to assign names to the sides. The “left-hand side” of an identity is denoted by LHS, and the “right-hand side” is denoted as RHS.

### Question 1

### Solution 1

Take LHS

*However we know that and we can transpose it to . By substituting this value of into our working we get:*

### Question 2

### Solution 2

Take the LHS

### Question 3

### Solution 3

Take the LHS

### Question 4

### Solution 4

Take the LHS

*However *

### Question 5

### Solution 5

Take the LHS