Question

find all value of sinx if 8sinx- cosx=4​

Answer 1

Heya

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put Sin x = z

Cos x = √ ( 1 - z² )

=>

8z - √(1-z²) = 4

=>

(8z-4) = √(1-z²)

SQUARING BOTH SIDE'S

=>

(8z-4)² =1-z²

=>

64z² +16 -64z = 1 - z²

=>

65z² -64z + 15 = 0

=>

z = (64 + 14 )/130

OR

z = (64-14 ) /130

=>

z =3/5 OR z = 5/13

So, Sin x = 3/5 OR Sin x = 5/13

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total number of values of Sin x is 4