Solve the equation:
√3 sinx - cosx = √2
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Heya!!!
√3 Sin x - Cos x = √2
_____________________________
put Sin x = z => Cos x = √ ( 1 - z² )
=>
z√3 - √2 = √ ( 1 - z² )²
SQUARING BOTH SIDE'S.
=>
3z² + 2 - 2z√6 = ( 1 - z² )
=>
4z² - 2z√6 + 1 = 0
=>
z = ( √3 - 1 )/ 2√2 OR z = ( √ 3 + 1 )/2√2
BY USING QUADRATIC FORMULA.
Sin x = ( √3 - 1 ) /2√2
Sin ( x ) = Sin ( 15 )
x = 15°
OR
Sin x = ( √3 + 1 ) /2√2
=>
Sin x = Sin 75
x = 75°
√3 Sin x - Cos x = √2
_____________________________
put Sin x = z => Cos x = √ ( 1 - z² )
=>
z√3 - √2 = √ ( 1 - z² )²
SQUARING BOTH SIDE'S.
=>
3z² + 2 - 2z√6 = ( 1 - z² )
=>
4z² - 2z√6 + 1 = 0
=>
z = ( √3 - 1 )/ 2√2 OR z = ( √ 3 + 1 )/2√2
BY USING QUADRATIC FORMULA.
Sin x = ( √3 - 1 ) /2√2
Sin ( x ) = Sin ( 15 )
x = 15°
OR
Sin x = ( √3 + 1 ) /2√2
=>
Sin x = Sin 75
x = 75°
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