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Simplify the expression.

quantity cosine of x to the power of two plus sine of x to the power of two divided by quantity cotangent of x to the power of two minus cosecant of x to the power of two.

csc x
-1
1
sec x

Simplify the expression quantity cosine of x to the power of two plus sine of x to the power of two divided by quantity cotangent of x to the power of two minus class=

Respuesta :

jiujuan

Answer:

-1

Step-by-step explanation:

The simplification of the given expression[tex]\dfrac{cos^2 + sin^2}{cot^2 - csc^2}[/tex] is -1.

What are trigonometric identities?

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

Given expression;

[tex]\dfrac{cos^2 + sin^2}{cot^2 - csc^2}[/tex]

We know that

cos^2 + sin^2 = 1

Also, we know that

cot^2 - csc^2 = -1

So, putting the values

[tex]\dfrac{cos^2 + sin^2}{cot^2 - csc^2}\\\\\dfrac{1}{-1} = -1[/tex]

Hence, the simplification of the given expression[tex]\dfrac{cos^2 + sin^2}{cot^2 - csc^2}[/tex] is -1.

Learn more about trigonometric;

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