Quiz about Trigonometric Identities

Question 1

Simplify: $$\frac{ an x+\cot x}{\cot x}$$

Accepted Answer

$$\sec^2x$$

Answer

1

Answer

$$\csc^2x$$

Answer

$$\sin^2x$$

Question 2

Simplify: $$\cos x+ an x\cdot\sin x$$

Accepted Answer

sec x

Answer

csc x

Answer

sin x

Answer

cot x

Question 3

Simplify: $$\sin^3x+\sin x\cdot\cos^2x$$

Accepted Answer

sin x

Answer

cos x

Answer

tan x

Answer

csc x

Question 4

Simplify: $$\left(\cot x ight)\left(\csc x ight)\left( an x ight)\left(\sin x ight)$$

Accepted Answer

1

Answer

$$\cot^2x$$

Answer

$$	an^2x$$

Answer

$$\sin^2x$$

Question 5

$$\left(1-\cos^2 heta ight)\csc heta\ =\ 1$$

Accepted Answer

False

Answer

True

Question 6

Simplify the trig expression.

Accepted Answer

1

Answer

-1

Answer

cotx

Answer

cosx

Question 7

Select ALL answers that would complete the trigonometric identity/identities.

1 = ____________

Accepted Answer

$$\csc^2u-\cot^2u$$

Accepted Answer

$$\sec^2u- an^2u$$

Accepted Answer

$$\cos^2u+\sin^2u$$

Answer

$$\sin^2u-\cos^2u$$

Question 8

Simplify: $$\frac{\sin^2x+\cos^2x+\cot^2x}{1+ an^2x}$$

Accepted Answer

$$\cot^2x$$

Answer

$$	an^2x$$

Answer

$$\csc^2x$$

Answer

$$\sec^2x$$

Question 9

Select all the correct variations of the following pythagorean identity:

$$1+\cot^2 heta=\csc^2 heta$$

Accepted Answer

$$\cot^2 heta=\csc^2 heta-1$$

Accepted Answer

$$1=\csc^2 heta-\cot^2 heta$$

Answer

$$\cot^2 heta+\csc^2 heta=1$$

Answer

$$\cot^2 heta-\csc^2 heta=1$$

Question 10

Select all the correct variations of the following pythagorean identity:

$$1+ an^2 heta=\sec^2 heta$$

Accepted Answer

$$1=\sec^2 heta- an^2 heta$$

Accepted Answer

$$ an^2 heta=\sec^2 heta-1$$

Answer

$$ an^2 heta+\sec^2 heta=1$$

Answer

$$\sec heta- an heta=1$$

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