Question

2sin^2x + 2cos^2x = 4a, then a = ?
A. 4
B. 3
C. 2
D. 1
E. 1/2

Answer 1

Option E) is correct.

`a=(1)/(2)`

Explanation:

Given trignometric equation is
`2sin^(2)x + 2cos^(2)x = 4a`

To find the value of "a" from the given equation:

`2sin^(2)x + 2cos^(2)x = 4a`

Taking common number "2" outside the equation of left hand side

`2(sin^(2)x +cos^(2)x) = 4a`

`sin^(2)x +cos^(2)x =(4a)/(2)`

`sin^(2)x+cos^(2)x =2a`

( We know the trignometric formula
`sin^(2)\theta +cos^(2)\theta=1` here

`\theta=x` )

Therefore
`(1) =2a`

`(1)/(2) =a`

It can be written as

`a=(1)/(2)`

Therefore
`a=(1)/(2)`

Option E) is correct.

Answer 2

E. 1/2

Explanation:

Divide by 2, then make use of the Pythagorean identity for sine and cosine.

sin(x)^2 +cos(x)^2 = 2a

1 = 2a . . . . . . . sin²+cos²=1

1/2 = a