Answer:
Option E) is correct.
[tex]a=\frac{1}{2}[/tex]
Step-by-step explanation:
Given trignometric equation is [tex]2sin^{2}x + 2cos^{2}x = 4a[/tex]
To find the value of "a" from the given equation:
[tex]2sin^{2}x + 2cos^{2}x = 4a[/tex]
Taking common number "2" outside the equation of left hand side
[tex]2(sin^{2}x +cos^{2}x) = 4a[/tex]
[tex]sin^{2}x +cos^{2}x =\frac{4a}{2}[/tex]
[tex]sin^{2}x+cos^{2}x =2a[/tex]
( We know the trignometric formula [tex]sin^{2}\theta +cos^{2}\theta=1[/tex] here
[tex]\theta=x[/tex] )
Therefore [tex](1) =2a[/tex]
[tex]\frac{1}{2} =a[/tex]
It can be written as
[tex]a=\frac{1}{2}[/tex]
Therefore [tex]a=\frac{1}{2}[/tex]
Option E) is correct.
