Question

2sinx square -3sin
x+1=0​

Answer 1

Step-by-step explanation:

Given :-

2 Sin² X - 3 Sin X + 1 = 0

To find:-

Solve the equation ?

Solution :-

Given equation is 2 Sin² X - 3 Sin X + 1 = 0

=> 2 Sin² X - 2 Sin X - Sin X + 1 = 0

=> 2 Sin X ( Sin X - 1 ) - 1 ( Sin X - 1 ) = 0

=> ( Sin X - 1 ) ( 2 Sin X - 1 ) = 0

=> ( Sin X - 1 ) = 0 (or) ( 2 Sin X - 1 ) = 0

=> Sin X = 1 (or) 2 Sin X = 1

=> Sin X = 1 (or) Sin X = 1/2

=> Sin X = Sin 90° (or) Sin X = Sin 30°

=>X = 90° (or) X = 30°

Answer:-

The roots of the given equation are 30° and 90°

Check:-

I) If X = 30° then

LHS = 2 Sin²30°-3 Sin 30° +1

=> 2 (1/2)²-3(1/2)+1

=> 2(1/4)-(3/2)+1

=> (2/4)-(3/2)+1

=> (1/2)-(3/2)+1

=> (1-3)/2 +1

=> (-2/2)+1

=> -1+1

=> 0

=> RHS

LHS = RHS is true for X = 30°

and

ii)If X = 90° then

LHS = 2 Sin²90°-3 Sin 90° +1

=> 2 (1)²-3(1)+1

=> 2(1)-(3)+1

=> 2-3+1

=> 3-3

=> 0

=> RHS

LHS = RHS is true for X = 90°

Used formulae:-

• Sin 30° = 1/2

• Sin 90° = 1

• Since it is a quadratic equation,it has two roots .