Trig identities are ready-made formulas that help you convert complex trigonometric expressions into simpler forms. Think of them as shortcuts that save time in calculations
sin²θ + cos²θ = 1 2. From this: 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ 3
- sin2θ = 2sinθcosθ - cos2θ = cos²θ - sin²θ = 2cos²θ - 1 = 1 - 2sin²θ - tan2θ = 2tanθ/(1 - tan²θ) 4
- sin(A + B) = sinAcosB + cosAsinB - sin(A - B) = sinAcosB - cosAsinB - cos(A + B) = cosAcosB - sinAsinB - cos(A - B) = cosAcosB + sinAsinB
verification of identities, simplification of expressions, finding values using identities, and proving given equations. Questions often combine multiple identities in one problem
Whenever you see sin²θ or cos²θ in an expression, immediately think of replacing them using sin²θ + cos²θ = 1. This often simplifies complex expressions instantly.
Use double angle identities cos2θ = 1 - 2sin²θ, so 1 - cos2θ = 1 - (1 - 2sin²θ) = 2sin²θ sin2θ = 2sinθcosθ
Substitute in the expression (1 - cos2θ)/(sin2θ) = (2sin²θ)/(2sinθcosθ)
Cancel and simplify = (2sin²θ)/(2sinθcosθ) = sinθ/cosθ = tanθ Answer: tanθ Another
- Complementary Angles: Remember that sin(90° - θ) = cosθ and cos(90° - θ) = sinθ. This helps in many substitution problems.
Students often forget the signs in sum and difference formulas. Remember: sin has same signs pattern (+, +, -, +), while cos alternates signs (+, -, +, -). Also, never mix up sin²θ + cos²θ = 1 with tan²θ + 1 = sec²θ - the order matters! The key to mastering trig identities is recognizing patterns and knowing which identity to apply when.
Practice identifying the base form of complex expressions.
10graded MCQs · easy to hard · full solution & trap analysis