RECAP OF TRIGONOMETRIC FORMULAE - CLASS 11

CONCEPTS AND FORMULAE TO RECOLLECT IN TRIGONOMETRY

1) sin² A + cos² A = 1 

2) 1 + tan²A = sec²A 

3) 1 + cot²A = cosec²A                                                                    

COMPOUND ANGLE FOR 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)
• Cot (A+B) =( cotAcotB -1)\(cotA + cotB)
• Cot (A-B) =( cotAcotB +1) \( cotB-cotA)

WHEN A=B ,                                                    

• Sin2A = 2sinA cosA
• Cos2A = cos²A-sin²A =2cos²A-1 =1-2sin²A
• Tan2A = 2tanA\ 1-tan²A 
• Cot 2A =( cot²A -1)\ 2cotA
• Cos²A =( 1+cos2A)\2
• Sin²A = ( 1-cos2A)\2

• Sin2A =2tanA\(1+tan²A)
• Cos2A =1-tan²A\(1+tan²A)

WHEN B=2A

      1) Sin3A =3sinA – 4sin³A

      2) Cos3A =4cos³A-3cosA

      3) Tan3A=( 3tanA- tan³A)\(1-3tan²A)

SUM TO PRODUCT FORMULAE

1) SinA+SinB = 2sin(A+B)\2.cos(A-B)\2

2) SinA-sinB = 2cos(A+B)\2.sin(A-B)\2

3) cosA+cosB =2cos(A+B)\2.cos(A-B)\2

4) cosA-cos B  =-2sin(A+B)\2.sin(A-B)\2

PRODUCT TO SUM FORMULAE

• 2sinAcosB = sin(A+B) + sin(A-B) = sin(sum) +sin(diff)
• 2cosA sinB = sin(A+B) – sin(A-B) =sin(sum) -sin(diff)
• 2cosA cosB = cos(A+B) + cos(A-B) = cos (sum) +cos(diff)
• 2sinA sinB = cos (A-B) -cos(A+B) =cos (diff) -cos(sum)

SOME SPECIAL FORMULAE

• Sin²A -sin²B = sin(A+B). sin(A-B) = cos²B- cos²A
• Cos²A – sin²B = cos(A+B). cos(A-B) =cos²B- sin²A

TRIG RATIOS OF SOME STANDARD ANGLES

• Sin 75 =( √3 +1) \2√2 = cos 15
• Cos75 =( √3-1)\2√2 = sin15
• Sin18 =( √5 – 1)\4 =cos 72
• Cos 36 = (√5 + 1)\4 = sin 54

HALF ANGLE FORMULAE

1) sin A = 2sinA\2 . cos A\2

2) cos A = cos²A\2 – sin²A\2  = 1- 2sin²A\2 =  2cos²A\2-1

3) TanA = 2tanA\2 \(1-tan²A\2)

4) sin²A\2 = (1-cosA)\2

5) Cos²A\2 = (1+cosA)\2

6) TanA\2  =√(1- cos A)\√(1+cosA)

7) sinA = 2tanA\2 \(1+tan²A\2)

8) CosA = (1-tan²A\2)\(1+tan²A\2)