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.


cos2θ + sin2θ = 1
1 + tan2θ = sec2θ
cot2θ + 1 = cosec2θ
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