🚀 Ethics (GS-IV) 7 Years (2017-2023) UPSC PYQs Solution Booklet 2024

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✍️ Trigonometry formula

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)