Question

If sin theta + cos theta equals to 1/2 then find the value of sin 2 theta

Answer 1

Given : sin∅ + cos∅ = ½

→ sin²∅ + cos²∅ + 2·sin∅·cos∅ = ¼

→ 1 + 2·sin∅·cos∅ = ¼

→ 2·sin∅·cos∅ = - ¾

→ sin∅ × cos∅ = - ⅜

→ sin∅ = - 3/(8cos∅)

→ - 3/(8cos∅) + cos∅ = ½

→ (- 3 + 8cos²∅)/(8cos∅) = ½

→ 8cos²∅ - 4cos∅ - 3 = 0

• D = b² - 4ac
• D = 16 + 96 = 112

→ cos∅ = (4 ± √112)/16

→ cos∅ = (4 + 8√2)/16

→ cos∅ = (1 + 2√2)/4

→ sin∅ = ½ - (1 + 2√2)/4

→ sin∅ = (2 - 1 - 2√2)/4

→ sin∅ = (1 - 2√2)/4

→ sin2∅ = (1 - 2√2)/2

OR ½ - √2