How do you simplify $1 - 4 {sin}^{2} x {cos}^{2} x$ $1-4sin^2xcos^2x$ ?

Question

How do you simplify $1 - 4 {sin}^{2} x {cos}^{2} x$ $1-4sin^2xcos^2x$ ?

1 Answer

Related questions

How do you use the fundamental trigonometric identities to determine the simplified form of the...
How do you apply the fundamental identities to values of $θ$ $theta$ and show that they are true?
How do you use the fundamental identities to prove other identities?
What are even and odd functions?
Is sine, cosine, tangent functions odd or even?
How do you simplify $sec x cos (\frac{π}{2} - x)$ $sec xcos (frac{\pi}{2} - x )$ ?
If $csc z = \frac{17}{8}$ $csc z = \frac{17}{8}$ and $cos z = - \frac{15}{17}$ $cos z= - \frac{15}{17}$ , then how do you find $cot z$ $cot z$ ?
How do you simplify $\frac{{sin}^{4} θ - {cos}^{4} θ}{{sin}^{2} θ - {cos}^{2} θ}$ $\frac{\sin^4 \theta - \cos^4 \theta}{\sin^2 \theta - \cos^2 \theta}$ using...
How do you prove that tangent is an odd function?
How do you prove that $sec (\frac{π}{3}) tan (\frac{π}{3}) = 2 \sqrt{3}$ $sec(pi/3)tan(pi/3)=2sqrt(3)$ ?

Impact of this question

19471 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-24T18:55:04

It can be simplified to ${cos}^{2} (2 x)$ $cos^2(2x)$ or $\frac{1}{2} (cos 4 x + 1)$ $1/2(cos4x+1)$

Explanation:

We have that

$1 - 4 {sin}^{2} x \cdot {cos}^{2} x = (1^{2} - {(2 cos x \cdot sin x)}^{2}) = (1 - {(sin 2 x)}^{2}) = {cos}^{2} (2 x)$ $1-4sin^2x*cos^2x=(1^2-(2cosx*sinx)^2)=(1-(sin2x)^2)=cos^2(2x)$

Also we know that

$cos (4 x) = 2 \cdot {cos}^{2} (2 x) - 1 \Rightarrow {cos}^{2} (2 x) = \frac{1}{2} (cos 4 x + 1)$ $cos(4x)=2*cos^2(2x)-1=>cos^2(2x)=1/2(cos4x+1)$

Remarks

It is known that : ${sin}^{2} (2 x) + {cos}^{2} (2 x) = 1$ $sin^2(2x)+cos^2(2x)=1$

Science

Math

Humanities

... and beyond

How do you simplify $1 - 4 {sin}^{2} x {cos}^{2} x$ $1-4sin^2xcos^2x$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you simplify 1−4sin2xcos2x1-4sin^2xcos^2x?

1 Answer

Explanation:

Related questions

Impact of this question

How do you simplify $1 - 4 {sin}^{2} x {cos}^{2} x$ $1-4sin^2xcos^2x$ ?