ICSE Class 10 Maths: Trigonometry — Identities & Notes 2026

Trigonometric Ratios

• In right-angled triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent
• Reciprocal ratios: cosec = 1/sin, sec = 1/cos, cot = 1/tan
• SOHCAHTOA mnemonic for remembering ratios

Standard Angle Values

• θ = 0°, 30°, 45°, 60°, 90° — memorise exact values as fractions/surds
• sin 30° = ½, cos 30° = √3/2, tan 30° = 1/√3; sin 45° = 1/√2; sin 60° = √3/2
• sin increases from 0 to 1 as θ goes 0° to 90°; cos decreases

Trigonometric Identities

• Pythagorean: sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ
• Complementary angles: sin θ = cos(90°−θ); tan θ = cot(90°−θ)
• ICSE: prove identities by converting both sides to sin and cos

Proving Trigonometric Identities

• Strategy: work on one (more complex) side; convert to sin/cos; simplify
• Key technique: multiply numerator and denominator by (1+cos θ) or similar conjugate
• Never cross-multiply when proving identities — treat LHS and RHS separately

Heights and Distances

• Angle of elevation: angle above horizontal looking up at an object
• Angle of depression: angle below horizontal looking down at an object
• Draw a clear diagram; set up right-angled triangles; apply appropriate trig ratio

Numericals — Heights and Distances

• Height of tower: angle of elevation from point on ground 50 m away is 30° — find height
• Two poles of unequal height; find distance between them given angles of elevation from base
• Height of cliff from two angles observed at two different distances

ICSE Exam Tips — Trigonometry

• Write identity to be proved at top; show each step clearly for full marks
• Always draw and label diagram for H&D problems
• Common error: confusing angle of elevation and depression in multi-step problems