How do you simplify cos(21) tan^2?

To simplify the expression cos(21) tan²(21), we start by recalling the definition of the tangent function. The tangent of an angle can be expressed as the ratio of the sine and cosine of that angle:

tan(21) = sin(21) / cos(21)

So, when we square the tangent function, we have:

tan²(21) = (sin(21) / cos(21))² = sin²(21) / cos²(21)

Now, substituting this back into the original expression gives us:

cos(21) tan²(21) = cos(21) * (sin²(21) / cos²(21))

This simplifies to:

cos(21) * (sin²(21) / cos²(21)) = (cos(21) * sin²(21)) / cos²(21)

Finally, we can cancel one of the cos(21) terms:

(sin²(21) / cos(21))

This further simplifies to:

sin²(21) * sec(21)

So, the simplified form of cos(21) tan²(21) is sin²(21) * sec(21).