SSC Trigonometry Formula PDF For Preparation

Trigonometry Formulas For SSC Exams

Type

Formula / Expression

Notes

Basic Ratios

sin θ = Opposite / Hypotenuse

Fundamental ratio

cos θ = Adjacent / Hypotenuse

Fundamental ratio

tan θ = Opposite / Adjacent

Fundamental ratio

cosec θ = 1 / sin θ = Hypotenuse / Opposite

Reciprocal of sin

sec θ = 1 / cos θ = Hypotenuse / Adjacent

Reciprocal of cos

cot θ = 1 / tan θ = Adjacent / Opposite

Reciprocal of tan

Pythagorean Identities

sin²θ + cos²θ = 1

Basic identity

1 + tan²θ = sec²θ

Derived from sin² + cos²

1 + cot²θ = cosec²θ

Derived from sin² + cos²

Sum & Difference

sin(A ± B) = sin A cos B ± cos A sin B

Use + for sum, − for difference

cos(A ± B) = cos A cos B ∓ sin A sin B

Use − for sum, + for difference

tan(A ± B) = (tan A ± tan B) / (1 ∓ tan A tan B)

Use − in the denominator for the sum

Double Angle

sin 2A = 2 sin A cos A

Useful for 2x problems

cos 2A = cos²A − sin²A = 2 cos²A − 1 = 1 − 2 sin²A

Multiple forms

tan 2A = 2 tan A / (1 − tan²A)

Direct formula

Half Angle

sin²(A/2) = (1 − cos A)/2

Memorise for half-angle problems

cos²(A/2) = (1 + cos A)/2

Memorise for half-angle problems

tan²(A/2) = (1 − cos A)/(1 + cos A)

Simplifies calculations

Special Values

sin 0°=0, sin 30°=1/2, sin 45°=1/√2, sin 60°=√3/2, sin 90°=1

Common angles for SSC

cos 0°=1, cos 30°=√3/2, cos 45°=1/√2, cos 60°=1/2, cos 90°=0

Common angles for SSC

tan 0°=0, tan 30°=1/√3, tan 45°=1, tan 60°=√3, tan 90°=Undefined

Common angles for SSC