Question

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

Answer 1

Answer:

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

Step-by-step 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 = - $\frac{1}{2}$

Or,   Ф = $sin^{-1}(-\frac{1}{2})$ = - 30°

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