Sure, I can help with that. The given function is y = cos⁴ t - sin⁴ t.

We can simplify this using the Pythagorean identity sin² t + cos² t = 1 and the double angle formula for cosine, cos(2t) = 1 - 2sin² t.

First, rewrite cos⁴ t - sin⁴ t as (cos² t)² - (sin² t)².

This is a difference of squares, which can be factored into (cos² t - sin² t)(cos² t + sin² t).

We know that cos² t + sin² t = 1, so we can substitute that in to get (cos² t - sin² t)(1).

Finally, we can use the double angle formula for cosine to simplify cos² t - sin² t to cos(2t).

So, y = cos⁴ t - sin⁴ t simplifies to y = cos(2t).

Question

Sure, I can help with that. The given function is y = cos⁴ t - sin⁴ t.

We can simplify this using the Pythagorean identity sin² t + cos² t = 1 and the double angle formula for cosine, cos(2t) = 1 - 2sin² t.

First, rewrite cos⁴ t - sin⁴ t as (cos² t)² - (sin² t)².

This is a difference of squares, which can be factored into (cos² t - sin² t)(cos² t + sin² t).

We know that cos² t + sin² t = 1, so we can substitute that in to get (cos² t - sin² t)(1).

Finally, we can use the double angle formula for cosine to simplify cos² t - sin² t to cos(2t).

So, y = cos⁴ t - sin⁴ t simplifies to y = cos(2t).

Knowee AI · Accepted Answer

Sure, I can help with that. The given function is y = cos⁴ t - sin⁴ t.

We can simplify this using the Pythagorean identity sin² t + cos² t = 1 and the double angle formula for cosine, cos(2t) = 1 - 2sin² t.

First, rewrite cos⁴ t - sin⁴ t as (cos² t)² - (sin² t)².

This is a difference of squares, which can be factored into (cos² t - sin² t)(cos² t + sin² t).

We know that cos² t + sin² t = 1, so we can substitute that in to get (cos² t - sin² t)(1).

Finally, we can use the double angle formula for cosine to simplify cos² t - sin² t to cos(2t).

So, y = cos⁴ t - sin⁴ t simplifies to y = cos(2t).

y = cos⁴ t - sin⁴ t