All Trigonometry formula For CDS, NDA AND SSC EXAMINATION

*Basic Formulas*

1. sin(A) = opposite side / hypotenuse

2. cos(A) = adjacent side / hypotenuse

3. tan(A) = opposite side / adjacent side

4. cot(A) = adjacent side / opposite side

5. sec(A) = hypotenuse / adjacent side

6. csc(A) = hypotenuse / opposite side

*Pythagorean Identities*

1. sin^2(A) + cos^2(A) = 1

2. tan^2(A) + 1 = sec^2(A)

3. cot^2(A) + 1 = csc^2(A)

*Sum and Difference Formulas*

1. sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

2. sin(A - B) = sin(A)cos(B) - cos(A)sin(B)

3. cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

4. cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

5. tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

6. tan(A - B) = (tan(A) - tan(B)) / (1 + tan(A)tan(B))

*Double Angle Formulas*

1. sin(2A) = 2sin(A)cos(A)

2. cos(2A) = cos^2(A) - sin^2(A)

3. tan(2A) = 2tan(A) / (1 - tan^2(A))

*Half Angle Formulas*

1. sin(A/2) = ±√((1 - cos(A)) / 2)

2. cos(A/2) = ±√((1 + cos(A)) / 2)

3. tan(A/2) = ±√((1 - cos(A)) / (1 + cos(A)))

*Product to Sum Formulas*

1. sin(A)cos(B) = (1/2)[sin(A + B) + sin(A - B)]

2. cos(A)cos(B) = (1/2)[cos(A + B) + cos(A - B)]

3. sin(A)sin(B) = (1/2)[cos(A - B) - cos(A + B)]

*Sum to Product Formulas*

1. sin(A) + sin(B) = 2sin((A + B)/2)cos((A - B)/2)

2. cos(A) + cos(B) = 2cos((A + B)/2)cos((A - B)/2)

3. sin(A) - sin(B) = 2cos((A + B)/2)sin((A - B)/2)

*Other Formulas*

1. sin(A) = cos(90 - A)

2. cos(A) = sin(90 - A)

3. tan(A) = cot(90 - A)