Question

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If Cos theta = x²+ 2x + 2 , then the values of theta and x can be ?

Answer 1

Hope this helps..........

Answer 2

cos∅ = x² + 2x + 2

we know

-1 ≤ cos∅ ≤ 1

so,

-1 ≤ x² +2x + 2 ≤ 1

now
case 1 :- x² +2x +2 ≤ 1

x² + 2x + 1 ≤ 0

( x + 1)² ≤ 0

but we know square never be negative
so, (x + 1)² = 0

x + 1 = 0

hence, x = - 1

case 2 :- -1 ≤ x² +2x +2

x² + 2x +3 ≥ 0

D = b² -4ac = (2)² -4(3)(1) < 0
coefficient of x² = 1 > 0

so, x² +2x +3 ≥ 0 for all real value .


so, common value of x in both cases
x = -1

hence, x = -1

now put x = -1 in cos∅ = x² +2x +2

cos∅ = (-1)² +2(-1) +2 = 1

cos∅ = 1
according to general solution of trigonometry ,
∅ = 2nπ where n is integer .