Let's review the trigonometric identities in A-Level Maths!

**Trigonometric Identities**

There are three reciprocal trigonometric functions, making a total of six including cosine, sine, and tangent.

The reciprocal cosine function is **secant**: secθ = 1/cosθ.

The reciprocal sine function is **cosecant**, cscθ = 1/sinθ.

The reciprocal tangent function is **cotangent**, expressed two ways: cotθ = 1/tanθ or cotθ = cosθ/sinθ.

**cos**^{2}**θ + sin**^{2}**θ = 1 **

**1 + tan**^{2}**θ = sec**^{2}**θ **

**cot**^{2}**θ + 1 = cosec**^{2}**θ **

When asked to show by counter-example that a statement is false, sub a value in and show that LHS is not equal to RHS.

**Formulae for sin (A + B), cos (A + B), tan (A + B)**

**Sin (A + B) = sin A cos B + cos A sin B**

**Sin (A - B) = sin A cos B - cos A sin B**

**Cos (A + B) = cos A cos B - sin A sin B**

**Cos (A - B) = cos A cos B + sin A sin B**

Also, we see that sin(π/2-x) = cos(x), cos(π/2-x) = sin(x);

that sin(x + π) = −sin(x), cos(x + π) = −cos(x);

and that sin(π − x) = sin(x), cos(π − x) = −cos(x).

The formulas also give the tangent of a difference formula, for tan(alpha − beta).

**Half-angle, double-angle**

**Double-angle identities derivation**

**Half-angle identities derivation**

Drafted by Eunice (Maths)

References:

https://www.onlinemathlearning.com/half-angle-examples.html

https://www.onlinemathlearning.com/double-angle-formula.html