if sinb/2-cosb/2=1/5 find the value of root sinb/2
Answers
Answered by
3
√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
Learn more:
sin x + cos x -1
https://brainly.in/question/12563868
cosX-4sinx=1 then sinx+4cosx[tex] cos(x) - Brainly.in
https://brainly.in/question/8892362
prove that 2sinxcosx-cosx/1 -sinx+sin^2x-cos^2x=cotx
https://brainly.in/question/3338788
Similar questions