"Simplify 4cos2(2x)−4cos2(x)+3sin2(x)4sin2(x)−sin2(2x)" was answered by students like you

Lennie Davis

Answered question

2022-01-16

Simplify

\frac{4 \cos^{2} (2 x) - 4 \cos^{2} (x) + 3 \sin^{2} (x)}{4 \sin^{2} (x) - \sin^{2} (2 x)}

David Clayton

Beginner2022-01-17Added 36 answers

\frac{4 \cos^{2} (2 x) - 4 \cos^{2} (x) + 3 \sin^{2} (x)}{4 \sin^{2} (x) - \sin^{2} (2 x)} = \frac{4 {(1 - 2 \sin^{2} x)}^{2} - 4 (1 - \sin^{2} x) + 3 \sin^{2} x}{4 \sin^{2} x - {(2 \sin x \cos x)}^{2}}

= \frac{4 - 16 \sin^{2} x + 16 \sin^{4} x - 4 + 4 \sin^{2} x + 3 \sin^{2} x}{4 \sin^{4} x}

= \frac{16 \sin^{4} x - 9 \sin^{2} x}{4 \sin^{4} x}

= 4 - \frac{9}{4} \csc^{2} x

boronganfh

Beginner2022-01-18Added 33 answers

Let us express everything in term of

s = \sin x

\frac{4 {(1 - 2 s^{2})}^{2} - 4 (1 - s^{2}) + 3 s^{2}}{4 s^{2} - 4 s^{2} (1 - s^{2})} = \frac{16 s^{4} - 9 s^{2}}{4 s^{4}} = 4 - \frac{9}{4 s^{2}}

alenahelenash

Expert2022-01-24Added 556 answers

Another way is to express everything in terms of

\cos 2 x

\frac{4 \cos^{2} 2 x - 3 (\cos^{2} x - \sin^{2} x) - \cos^{2} x}{4 \cdot \frac{1 - \cos 2 x}{2} - (1 - \cos^{2} 2 x)}

= \frac{4 \cos^{2} 2 x - 3 \cos 2 x - \frac{1 + \cos 2 x}{2}}{2 (1 - \cos 2 x) + \cos^{2} 2 x - 1}

= \frac{8 \cos^{2} 2 x - 7 \cos 2 x - 1}{2 (\cos 2 x - 1)^{2}}

= \frac{(8 \cos 2 x + 1) (\cos 2 x - 1)}{2 (2 \cos 2 x - 1)^{2}}

= \frac{8 \cos 2 x + 1}{2 \cos 2 x - 2}

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?