**CONCEPTS AND FORMULAE TO RECOLLECT IN TRIGONOMETRY**

1) sin^{2 }A + cos^{2 }A = 1

2) 1 + tan^{2}A = sec^{2}A

3) 1 + cot^{2}A = cosec^{2}A

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 = cos
^{2}A-sin^{2}A =2cos^{2}A-1 =1-2sin^{2}A - Tan2A = 2tanA\ 1-tan
^{2}A - Cot 2A =( cot
^{2}A -1)\ 2cotA - Cos
^{2}A =( 1+cos2A)\2 - Sin
^{2}A = ( 1-cos2A)\2

- Sin2A =2tanA\(1+tan
^{2}A) - Cos2A =1-tan
^{2}A\(1+tan^{2}A)

WHEN B=2A

1) Sin3A =3sinA – 4sin^{3}A

2) Cos3A =4cos^{3}A-3cosA

3) Tan3A=( 3tanA- tan^{3}A)\(1-3tan^{2}A)

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**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)

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**SOME SPECIAL FORMULAE**

- Sin
^{2}A -sin^{2}B = sin(A+B). sin(A-B) = cos^{2}B- cos^{2}A - Cos
^{2}A – sin^{2}B = cos(A+B). cos(A-B) =cos^{2}B- sin^{2}A

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**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

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**HALF ANGLE FORMULAE**

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

2) cos A = cos^{2}A\2 – sin^{2}A\2 = 1- 2sin^{2}A\2 = 2cos^{2}A\2-1

3) TanA = 2tanA\2 \(1-tan^{2}A\2)

4) sin^{2}A\2 = (1-cosA)\2

5) Cos^{2}A\2 = (1+cosA)\2

6) TanA\2 =√(1- cos A)\√(1+cosA)

7) sinA = 2tanA\2 \(1+tan^{2}A\2)

8) CosA = (1-tan^{2}A\2)\(1+tan^{2}A\2)