Sin4A - cos4A = sin2A - cos2A
Can i just square root the left side??:O
I don't think it is an identity.
let A=90 deg
sin(360)-cos(360)=0-1
sin(180)-cos(180)=0+1
The sides are not equal.
?? Im sorry i don't understand what u did but im sure that this is an identity we have to prove that the left side equals the right side:)
No, you cannot simply square root the left side of the equation. The equation you provided, sin4A - cos4A = sin2A - cos2A, involves trigonometric functions and their respective angles.
To solve this equation, you need to apply trigonometric identities and simplify both sides of the equation separately.
Let's start with the left side of the equation, sin4A - cos4A:
1. Apply the double-angle identity for sine: sin2θ = 2sinθcosθ
- We can rewrite sin4A as (sin2A)(sin2A).
2. Apply the double-angle identity for cosine: cos2θ = cos^2θ - sin^2θ
- We can rewrite cos4A as (cos2A)(cos2A) - (sin2A)(sin2A).
Combining these identities, the left side of the equation becomes:
(sin2A)(sin2A) - [(cos2A)(cos2A) - (sin2A)(sin2A)]
Next, let's simplify the right side of the equation, sin2A - cos2A:
1. Apply the double-angle identities for sine and cosine, similar to the steps above.
After simplifying both sides, you can then compare if they are equal. Note that taking the square root of both sides of an equation is not a valid operation unless you have already simplified both sides to a perfect square form.