Simplify the expression. sine of x to the second power minus one divided by cosine of negative x

Solution:

Given that:

sine of x to the second power minus one divided by cosine of negative x.

Hence we can express it as:

⇒ (sin x)² - 1/cos (-x)

From trigonometry,

We know that,

(sin x)² = sin²x and cos(-x) = cos x

Also,

1/cos x = sec x

Therefore,

(sin x)² - 1/cos (-x) = sin²x - sec x

Simplify the expression. sine of x to the second power minus one divided by cosine of negative x

Summary:

The simplified form of the given expression sine of x to the second power minus one divided by cosine of negative x is sin²x - sec x.