Question

all values of a for which the equation sin^4x+cos^4x +sin2x
+a=0 is valid

Answer 1

@myininaya @amistre64 @ganeshie8

Answer 2

@paki

Answer 3

\[\begin{align}\sin^4x + \cos^4x &= (1-\cos^2x)^2 + \cos^4x \\~\\&= 2\cos^4x -2\cos^2x + 1 \\~\\&= \frac{1}{2}(2\cos^2x-1)^2 + \frac{1}{2} \\~\\&= \dfrac{\cos^2(2x)+1}{2} \end{align} \]

Answer 4

plug that result in the given equation, you will see a quadratic in sin(2x)

Answer 5

after that use below to restrict \(a\) :
1) \(\large D \ge 0\)
2) \(\large |\sin(2x)| \le 1\)

Answer 6

if everything goes well, you should endup with \(\large -1.5\le a\le 0.5\)