Question

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

Answer 1

Answer:

Option E) is correct.

$a=\frac{1}{2}$

Step-by-step 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

$2(sin^{2}x +cos^{2}x) = 4a$

$sin^{2}x +cos^{2}x =\frac{4a}{2}$

$sin^{2}x+cos^{2}x =2a$

( We know the trignometric formula  $sin^{2}\theta +cos^{2}\theta=1$ here

$\theta=x$  )

Therefore  $(1) =2a$

$\frac{1}{2} =a$

It can be written as

$a=\frac{1}{2}$

Therefore  $a=\frac{1}{2}$

Option E) is correct.

Answer 2

Answer:

  E.  1/2

Step-by-step 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