Question

Sinx + 1/Sinx = 7/2√3 .Find x

Answer 1

Good Morning!!

Sin x + 1/Sin x = 7/2√3

let Sin x = y

y + 1/y = 7/2√3

y² + 1 = 7y/2√3

2√3y² - 7y + 2√3 = 0

2√3y² - 4y - 3y + 2√3 = 0

2y ( √3y - 2 ) -√3 ( √3y - 2 ) = 0

( 2y - √3 ) = 0 OR ( √3y - 2 ) = 0

y = √3/2 OR y = 2/√3

Sin x = √3/2 OR Sin x = 2/√3

Sin x = Sin 60 OR x = Sin-¹ ( 2/√3 )

Becoz Sin 60 = √3/2

x = 60° OR x = Sin-¹ (2/√3 )