Chapter 3: Trigonometric Functions

Key Identities:
• sin²x + cos²x = 1
• 1 + tan²x = sec²x
• 1 + cot²x = cosec²x
• sin(A±B) = sinA cosB ± cosA sinB

Q1. Find the value of sin 75°.

Solution

sin 75° = sin(45° + 30°)
= sin45²cos30 + cos45²sin30
= (√2/2)(√3/2) + (√2/2)(1/2)
= (√6 + √2)/4

Q2. Prove: (sinx + cosx)² = 1 + sin2x.

Solution

LHS = sin²x + cos²x + 2sinx cosx = 1 + sin2x = RHS ✓

Q3. Solve: sin x = 1/2 for x in [0, 2π].

Solution

x = π/6 or x = 5π/6