msr8ahhhhhmer
contestada

Which of the following is not an identity?

A. cos^2 x csc x - csc x = -sin x

B. sin x(cot x + tan x) = sec x

C. cos^2 x - sin^2 x = 1- 2sin^2 x

D. csc^2 x + sec^2 x = 1

Respuesta :

HomertheGenius
A ) cos² x · 1 / sin x - 1 / sin x = - sin x
cos² x - 1 / sin x = - sin x 
- sin² x / sin x = - sin x
- sin x = - sin x     ( correct )
B ) sin x ( cos x / sin x + sin x / cos x ) = 1 / cos x
sin x · ( cos² x + sin²x ) / sin x cos x = 1 / cos x
sin x · 1 / sin x cos x = 1 / cos x
1 / cos x = 1 / cos x  ( correct )
C ) cos² x - sin² x = 1 - 2 sin² x
1 - sin² x - sin² x = 1 - 2 sin² x
1 - 2 sin² x = 1 - 2 sin² x   ( correct )
D ) 1/sin²x + 1/ cos²x = 1
cos²x + sin² x / sin² x cos² x = 1
1 / cos² x sin² x = 1
cos²x sin² x ≠ 1
Answer: D ) is not an identity. 
mickymike92

Since the two sides of the equation are not equal, the equation 1/sin²x + 1/ cos²x = 1 is not an identity.

What are trigonometric identities?

Trigonometric identities are equations that are true for the trigonometric functions

They are based on the six trigonometric functions: sine, cosine, tangent, secant, cosecant, and cotangent.

The given equations are solved to determine if they are identities as follows:

A ) cos² x · 1 / sin x - 1 / sin x = - sin x

cos² x - 1 / sin x = - sin x 

- sin² x / sin x = - sin x

- sin x = - sin x

The equation is an identity

B ) sin x ( cos x / sin x + sin x / cos x ) = 1 / cos x

sin x · ( cos² x + sin²x ) / sin x cos x = 1 / cos x

sin x · 1 / sin x cos x = 1 / cos x

1 / cos x = 1 / cos x

The equation is an identity

C ) cos² x - sin² x = 1 - 2 sin² x

1 - sin² x - sin² x = 1 - 2 sin² x

1 - 2 sin² x = 1 - 2 sin² x

The equation is an identity

D ) 1/sin²x + 1/ cos²x = 1

cos²x + sin² x / sin² x cos² x = 1

1 / cos² x sin² x = 1

cos²x sin² x ≠ 1

The equation is not an identity.

Therefore, the equation 1/sin²x + 1/ cos²x = 1 is not an identity.

Learn more about trigonometric identities at: https://brainly.com/question/7331447

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