Homework PracticeSign Up
Back to assignmentPrintable assignment view
Print options

Homework Practice

Printable assignment

Trigonometric Identities Practice 3: Mixed Simplification

Section A: Mixed Identity Use

Question 1mcq
If sin⁡A=817\sin A=\frac{8}{17} for acute AA, find cot⁡A\cot A.
A.178\frac{17}{8}
B.1517\frac{15}{17}
C.158\frac{15}{8}
D.815\frac{8}{15}
Question 2mcq
Simplify tan⁡2A+1−sec⁡2A\tan^2A+1-\sec^2A.
A.sec⁡2A\sec^2A
B.00
C.11
D.tan⁡2A\tan^2A
Question 3mcq
Which transformation proves cos⁡A1−sin⁡A=1+sin⁡Acos⁡A\frac{\cos A}{1-\sin A}=\frac{1+\sin A}{\cos A}?
A.Multiply numerator and denominator on the left by 1+sin⁡A1+\sin A.
B.Cancel 11 from 1−sin⁡A1-\sin A.
C.Replace cos⁡A\cos A with sin⁡A\sin A.
D.Set A=0∘A=0^\circ only.
Question 4mcq
Simplify sec⁡Atan⁡A\frac{\sec A}{\tan A}.
A.sin⁡A\sin A
B.cos⁡A\cos A
C.cot⁡A\cot A
D.cosec⁡A\cosec A
Question 5mcq
Simplify 1−cos⁡2A1+cos⁡A\frac{1-\cos^2A}{1+\cos A}.
A.sin⁡A\sin A
B.cos⁡A\cos A
C.1−cos⁡A1-\cos A
D.1+cos⁡A1+\cos A

Section B: Restrictions and Errors

Question 6mcq
In simplifying 1−cos⁡2A1+cos⁡A\frac{1-\cos^2A}{1+\cos A}, which restriction is needed for cancellation?
A.cos⁡A=1\cos A=1 only
B.1+cos⁡Aeq01+\cos A eq0
C.sin⁡A=0\sin A=0
D.tan⁡A=1\tan A=1
Question 7mcq
A student writes sin⁡2A=sin⁡A\sqrt{\sin^2A}=\sin A for every angle. What is the issue?
A.Generally sin⁡2A=∣sin⁡A∣\sqrt{\sin^2A}=|\sin A|.
B.The square root is always negative.
C.sin⁡2A\sin^2A is never positive.
D.The correct value is always cos⁡A\cos A.
Question 8mcq
If sin⁡2A=716\sin^2A=\frac{7}{16}, what is cos⁡2A\cos^2A?
A.716\frac{7}{16}
B.2316\frac{23}{16}
C.34\frac{3}{4}
D.916\frac{9}{16}
Question 9mcq
From 1+tan⁡2A=sec⁡2A1+\tan^2A=\sec^2A, what is tan⁡2A\tan^2A equal to?
A.sec⁡A−1\sec A-1
B.1+sec⁡2A1+\sec^2A
C.sec⁡2A−1\sec^2A-1
D.1−sec⁡2A1-\sec^2A
Question 10mcq
From 1+cot⁡2A=cosec⁡2A1+\cot^2A=\cosec^2A, what is cot⁡2A\cot^2A equal to?
A.1+cosec⁡2A1+\cosec^2A
B.cosec⁡2A−1\cosec^2A-1
C.1−cosec⁡2A1-\cosec^2A
D.cosec⁡A−1\cosec A-1