Question

4cos^2(theta)+2sin(theta)=2

Answer 1

The value of given expression i.e Ф is 90° and - 30°

Explanation:

Given as :

4 cos²Ф + 2 sinФ = 2

∵ sin²Ф + cos²Ф = 1 , so , cos²Ф = 1 - sin²Ф

Or, 4 ( 1 - sin²Ф ) + 2 sinФ = 2

Or, 4 - 4 sin²Ф + 2 sinФ = 2

or, 4 sin²Ф - 2 sinФ - 4 + 2 = 0

or, 4 sin²Ф - 2 sinФ - 2 = 0

or, 2 sin²Ф - sinФ - 1 = 0

or, 2 sin²Ф - 2 sinФ + sinФ - 1 = 0

Or, 2 sinФ ( sinФ - 1 ) + 1 ( sinФ - 1 ) = 0

∴ ( sinФ - 1 ) ( 2 sinФ + 1 ) = 0

i.e ( sinФ - 1 ) = 0 And ( 2 sinФ + 1 ) = 0

since ( sinФ - 1 ) = 0

So, sinФ = 1

Or, Ф =
`sin^(-1)(1)` = 90°

And ( 2 sinФ + 1 ) = 0

Or, 2 sinФ = - 1

Or, sinФ = -
`(1)/(2)`

Or, Ф =
`sin^(-1)(-(1)/(2))` = - 30°

Hence the value of given expression i.e Ф is 90° and - 30° Answer