GRADE 12 TRIGONOMETRIC IDENTITIES &
SOLVING TRIGONOMETRIC EQUATIONS
Complete study notes with identities, strategies, and worked examples.
1. Basic Trigonometric Ratios
For an angle θ:
sinθ = opposite / hypotenuse
cosθ = adjacent / hypotenuse
tanθ = opposite / adjacent
Reciprocal Ratios:
cosecθ = 1/sinθ
secθ = 1/cosθ
cotθ = 1/tanθ
2. Fundamental Identities
Pythagorean Identities:
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
Quotient Identities:
tanθ = sinθ / cosθ
cotθ = cosθ / sinθ
Reciprocal Identities:
sinθ = 1/cosecθ
cosθ = 1/secθ
tanθ = 1/cotθ
3. Proving Trigonometric Identities
Goal: Show that LHS = RHS.
Rules:
• Work on ONE side only
SOLVING TRIGONOMETRIC EQUATIONS
Complete study notes with identities, strategies, and worked examples.
1. Basic Trigonometric Ratios
For an angle θ:
sinθ = opposite / hypotenuse
cosθ = adjacent / hypotenuse
tanθ = opposite / adjacent
Reciprocal Ratios:
cosecθ = 1/sinθ
secθ = 1/cosθ
cotθ = 1/tanθ
2. Fundamental Identities
Pythagorean Identities:
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
Quotient Identities:
tanθ = sinθ / cosθ
cotθ = cosθ / sinθ
Reciprocal Identities:
sinθ = 1/cosecθ
cosθ = 1/secθ
tanθ = 1/cotθ
3. Proving Trigonometric Identities
Goal: Show that LHS = RHS.
Rules:
• Work on ONE side only
