Question

sin2pie/3+sin2pie/4+sin 2 pi/6​

Answer 1

Given data : sin² π/3 + sin² π/4 + sin² π/6

Solution :

➜ sin² π/3 + sin² π/4 + sin² π/6

Here, we know that π = 180⁰

Now,

➜ sin² 180⁰/3 + sin² 180⁰/4 + sin² 180⁰/6

➜ sin² 60⁰ + sin² 45⁰ + sin² 30⁰

➜ (sin 60⁰)² + (sin 45⁰)² + (sin 30⁰)²

{Here,

• sin 60⁰ = √3/2
• sin 45⁰ = 1/√2
• sin 30⁰ = 1/2 }

➜ (1/√3)² + (1/√2)² + (1/2)²

➜ 1/3 + 1/2 + 1/4

➜ (1 * 2)/(3*2) + (1*3)/(2*3) + 1/4

➜ 2/6 + 3/6 + 1/4

➜ (2 + 3)/6 + 1/4

➜ 5/6 + 1/4

➜ (5 * 4)/(6 * 4) + (1 * 6)/(4 * 6)

➜ 20/24 + 6/24

➜ (20 + 6)/24

➜ 26/24

➜ 13/12

Answer : sin² π/3 + sin² π/4 + sin² π/6 = 13/12

More info :

• sin 0⁰ = 0
• sin 30⁰ = 1/2
• sin 45⁰ = 1/√2
• sin 60⁰ = √3/2
• sin 90⁰ = 1

• cos 0⁰ = 1
• cos 30⁰ = √3/2
• cos 45⁰ = 1/√2
• cos 60⁰ = 1/2
• cos 90⁰ = 0

• tan 0⁰ = 0
• tan 30⁰ = 1/√3
• tan 45⁰ = 1
• tan 60⁰ = √3
• tan 90⁰ = ∞ (infinity)