Trigonometric Identities Practice 1: Core Identities

Section A: Identity Foundations

Question 1mcq

Which statement best describes a trigonometric identity?

A.It is an equation with no variables.

B.It is always solved by substituting

45^\circ

.

C.It is true for all allowed values of the angle.

D.It is true for only one angle.

Question 2mcq

Which is an identity rather than an equation to solve for one value?

A.

\tan A=1

only for

A=45^\circ

B.

\sin^2 A+\cos^2 A=1

C.

\sin A=\frac12

D.

2x+3=7

Question 3mcq

In a right triangle, if

\sin A=\frac{\text{opposite}}{\text{hypotenuse}}

and

\cos A=\frac{\text{adjacent}}{\text{hypotenuse}}

, which theorem leads to

\sin^2A+\cos^2A=1

?

A.Pythagoras theorem

B.Basic Proportionality Theorem

C.Midpoint theorem

D.Equal tangents theorem

Question 4mcq

If

\sin A=\frac{3}{5}

for acute

A

, what is

\cos A

?

A.

\frac{2}{5}

B.

\frac{3}{4}

C.

\frac{5}{4}

D.

\frac{4}{5}

Question 5mcq

If

\cos A=\frac{12}{13}

for acute

A

, find

\sin A

.

A.

\frac{12}{5}

B.

\frac{5}{12}

C.

\frac{5}{13}

D.

\frac{1}{13}

Section B: Simplify and Check

Question 6mcq

To derive

1+\tan^2A=\sec^2A

from

\sin^2A+\cos^2A=1

, what should we divide by?

A.

\sec^2A

B.

\cos^2A

C.

\sin^2A

D.

\tan^2A

Question 7mcq

To derive

1+\cot^2A=\cosec^2A

, divide

\sin^2A+\cos^2A=1

by:

A.

\sin^2A

B.

\cos^2A

C.

\tan^2A

D.

\cosec^2A

Question 8mcq

Simplify

\sec^2A-\tan^2A

.

A.

0

B.

\sin^2A

C.

\cos^2A

D.

1

Question 9mcq

When deriving

1+\tan^2A=\sec^2A

, why must

\cos A eq0

?

A.Because tangent is always

0

.

B.Because

\sec A

is always

1

.

C.Because we divide by

\cos^2A

.

D.Because sine is never defined.

Question 10mcq

A student cancels

\sin A

from

\sin A+\cos A

and writes

1+\cos A

. What is wrong?

A.The result should be

\tan A

.

B.Terms in a sum cannot be cancelled like common factors.

C.

\sin A

is never cancellable because it is negative.

D.

\cos A

must be cancelled first.