Class 11 Trigonometry Formulas

Trigonometry Formulas

sin(−θ) = −sinθ
cos(−θ) = cosθ
tan(−θ) = −tanθ
cosec(−θ) = −cosecθ
sec(−θ) = secθ
cot(−θ) = −cotθ

Product to Sum Formulas

sin x sin y = 1/2 [cos(x–y) − cos(x+y)]
cos x cos y = 1/2[cos(x–y) + cos(x+y)]
sin x cos y = 1/2[sin(x+y) + sin(x−y)]
cos x sin y = 1/2[sin(x+y) – sin(x−y)]

Sum to Product Formulas

sin x + sin y = 2 sin [(x+y)/2] cos [(x-y)/2]
sin x – sin y = 2 cos [(x+y)/2] sin [(x-y)/2]
cos x + cos y = 2 cos [(x+y)/2] cos [(x-y)/2]
cos x – cos y = -2 sin [(x+y)/2] sin [(x-y)/2]

Identities

sin2 A + cos2 A = 1
1+tan2 A = sec2 A
1+cot2 A = cosec2 A

Basic Trigonometric Formulas

cos (A + B) = cos A cos B – sin A sin B
cos (A – B) = cos A cos B + sin A sin B
sin (A+B) = sin A cos B + cos A sin B
sin (A -B) = sin A cos B – cos A sin B

Based on the above addition formulas for sin and cos, we get the following below formulas:

sin(π/2-A) = cos A
cos(π/2-A) = sin A

sin(π-A) = sin A
cos(π-A) = -cos A
sin(π+A)=-sin A
cos(π+A)=-cos A

sin(2π-A) = -sin A
cos(2π-A) = cos A

If none of the angles A, B and (A ± B) is an odd multiple of π/2, then

tan(A+B) = [(tan A + tan B)/(1 – tan A tan B)]
tan(A-B) = [(tan A – tan B)/(1 + tan A tan B)]

If none of the angles A, B and (A ± B) is a multiple of π, then

cot(A+B) = [(cot A cot B − 1)/(cot B + cot A)]
cot(A-B) = [(cot A cot B + 1)/(cot B – cot A)]

Some additional formulas for sum and product of angles:

cos(A+B) cos(A–B)=cos2A–sin2B=cos2B–sin2A

sin(A+B) sin(A–B) = sin2A–sin2B=cos2B–cos2A

sinA+sinB = 2 sin (A+B)/2 cos (A-B)/2

Formulas for twice of the angles:

sin2A = 2sinA cosA = [2tan A + (1+tan2A)]

cos2A = cos2A–sin2A = 1–2sin2A = 2cos2A–1= [(1-tan2A)/(1+tan2A)]

tan 2A = (2 tan A)/(1-tan2A)