pure maths formulae

sin(A+B)

sinAcosB + cosAsinB

sin(A-B)

sinAcosB - cosAsinB

cos(A+B)

cosAcosB - sinAsinB

cos(A-B)

cosAcosB + sinAsinB

tan(A+B)

(tanA + tanB) / (1 - tanAtanB)

tan(A-B)

(tanA - tanB) / (1 + tanAtanB)

sin2A

2sinAcosA

cos2A

• cos²A - sin²A

• 2cos²A - 1

• 1 - sin²A

tan2A

(2tanA) / (1 - tan²A)

secx

1 / cosx

cosecx

1 / sinx

cotx

• 1 / tanx

• cosx / sinx

sec²x

1 + tan²x

cosec²x

1 + cot²x

f(x + a)

horizontal translation of -a

f(x) + a

vertical translation of +a

f(ax)

horizontal stretch by a scale factor of 1/a

af(x)

vertical stretch of a scale factor a

f(-x)

reflection in the y-axis

-f(x)

reflection in the x-axis

nth term of an arithmetic sequence

a + (n-1)d

sum of an arithmetic series

(n/2)(2a + (n-1)d)

nth term of geometric sequence

ar^n-1

sum of geometric series

a(1-rⁿ) / (1 - r)

sum to infinity

a / (1 - r)