Q1. Choose the correct option. (10×1=10)
Q2. Write down short answers of following questions. (15×2=30)
Q3. Write detailed answers of the following questions. (Answer any 2) (2×5=10)
1. Triangle Angle Identity
If α, β, γ are the angles of a triangle ABC, then prove that: cosec(α) = 1/sin(β + γ)
2. Trigonometric Product Identity
Find the values of sin 36° and cos 36° without using table or calculator. Hence prove that:
cos 36° cos 72° cos 108° cos 144° = 1/16
3. Trigonometric Expression
Let x = sin 15° + cos 15°, then:
(a) Show that x² = 1 + sin 30°;
(b) Hence compute x and then find sin 15° cos 15° and sin 75° cos 75°.