Question

if sinb/2-cosb/2=1/5 find the value of root sinb/2

Answer 1

√sin(b/2)  = 2/√5  if  sin(b/2)-cos(b/2)=1/5

Step-by-step explanation:

sin(b/2)-cos(b/2)=1/5

Let say √sin(b/2)  = x

Squaring both sides

sin(b/2)  = x²

cos(b/2) = √(1 - x⁴)

x² - √(1 - x⁴)  = 1/5

=> √(1 - x⁴) = x²  - 1/5

=> 5√(1 - x⁴)  = 5x²  - 1

Squaring both sides

=> 25(1 - x⁴)  = 25x⁴  + 1 - 10x²

=> 50x⁴ - 10x²  - 24 = 0

=> 25x⁴ - 5x²  - 12 = 0

=> 25x⁴ - 20x² + 15x² - 12 = 0

=> 5x²(5x² - 4) + 3(5x² - 4) = 0

=> (5x² + 3)(5x² - 4) = 0

=> x² = 4/5   or   x² = -3/5 ( -ve value of square not possible)

=> x = 2/√5

√sin(b/2)  = 2/√5

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