TRIGONOMETRY CLASS 11 ALL IMPORTANT IDENTITIES AND FORMULAS

Trigonometry Class 11 Formulas

sin(−θ)=−sinθ

cos(−θ)=cosθ

tan(−θ)=−tanθ

cosec(−θ)=−cosecθ

sec(−θ)=secθ

cot(−θ)=−cotθ

Product to Sum Formulas

sinx siny=12[cos(x–y)−cos(x+y)]

cosxcosy=12[cos(x–y)+cos(x+y)]

sinxcosy=12[sin(x+y)+sin(x−y)]

cosxsiny=12[sin(x+y)–sin(x−y)]

Sum to Product Formulas

sinx+siny=2sin(x+y2)cos(x−y2)

sinx−siny=2cos(x+y2)sin(x−y2)

cosx+cosy=2cos(x+y2)cos(x−y2)

cosx−cosy=–2sin(x+y2)sin(x−y2)

Identities

sin2 A + cos2 A = 1

1+tan2 A = sec2 A

1+cot2 A = cosec2 A

Sign of Trigonometric Functions in Different Quadrants

Quadrants→	I	II	III	IV
Sin A	+	+	–	–
Cos A	+	–	–	+
Tan A	+	–	+	–
Cot A	+	–	+	–
Sec A	+	–	–	+
Cosec A	+	+	–	–

Basic Trigonometric Formulas for Class 11

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 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)=tanA+tanB1–tanAtanB

tan(A–B)=tanA–tanB1+tanAtanB

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

cot(A+B)=cotAcotB−1cotB+cotAcot(A−B)=cotAcotB+1cotB−cotA

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=2sinA+B2cosA−B2

Formulas for twice of the angles:

sin2A=2sinAcosA=2tanA1+tan2A

cos2A=cosA–sin2A=1–2sin2A=2cos2A–1=1−tan2A1+tan2A

tan2A=2tanA1–tan2A

Formulas for thrice of the angles:

sin3A=3sinA–4sin3A=4sin(60∘−A).sinA.sin(60∘+A)

cos3A=4cos3A–3cosA=4cos(60∘−A).cosA.cos(60∘+A)

tan3A=3tanA–tan3A1−3tan2A=tan(60∘−A).tanA.tan(60∘+A)

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