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RECAP OF TRIGONOMETRIC FORMULAE - CLASS 11

Dhanalakshmi N.
06/08/2018 0 0

CONCEPTS AND FORMULAE TO RECOLLECT IN TRIGONOMETRY

 

1) sin2 A + cos2 A = 1 

2) 1 + tan2A = sec2

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-tan2
  • 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)

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