Trig Identities questions

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Trig Identities question collection

Review Trig Identities questions for Maths, with correct answers shown and coverage across \cos(180^\circ-x)=\; \cos(360^\circ-x)=\; \operatorname{sec}x=\.

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Question 1

\(\cos(-x)=\ ?\)
  1. \(\cos x\)
  2. \(-\cos x\)
  3. \(\sin x\)
  4. \(-\sin x\)

Question 2

\(\cos(180^\circ-x)=\ ?\)
  1. \(-\cos x\)
  2. \(\cos x\)
  3. \(\sin x\)
  4. \(-\sin x\)

Question 3

\(\cos(2x)=\ ?\)
  1. \(\cos^2(x)-\sin^2(x)\)
  2. \(\cos^2(x)+\sin^2(x)\)
  3. \(2\sin(x)\cos(x)\)
  4. \(1-2\cos^2(x)\)

Question 4

\(\cos(360^\circ-x)=\ ?\)
  1. \(\cos x\)
  2. \(-\cos x\)
  3. \(\sin x\)
  4. \(-\sin x\)

Question 5

\(\cos(A-B)=\ ?\)
  1. \(\cos A\cos B+\sin A\sin B\)
  2. \(\cos A\cos B-\sin A\sin B\)
  3. \(\sin A\cos B-\cos A\sin B\)
  4. \(\sin A\sin B-\cos A\cos B\)

Question 6

\(\cos(A+B)=\ ?\)
  1. \(\cos A\cos B-\sin A\sin B\)
  2. \(\cos A\cos B+\sin A\sin B\)
  3. \(\sin A\cos B+\cos A\sin B\)
  4. \(\sin A\sin B-\cos A\cos B\)

Question 7

\(\operatorname{sec}x=\ ?\)
  1. \(\operatorname{cosec}(90^\circ-x)\)
  2. \(\operatorname{cosec}(90^\circ+x)\)
  3. \(\tan(90^\circ-x)\)
  4. \(\operatorname{cosec}x\)

Question 8

\(\frac{\cos(x)}{\sin(x)}=\ ?\)
  1. \(\cot(x)\)
  2. \(\tan(x)\)
  3. \(\sec(x)\)
  4. \(\operatorname{cosec}(x)\)

Question 9

\(\frac{\sin(x)}{\cos(x)}=\ ?\)
  1. \(\tan(x)\)
  2. \(\cot(x)\)
  3. \(\sec(x)\)
  4. \(\operatorname{cosec}(x)\)

Question 10

\(\sin(-x)=\ ?\)
  1. \(-\sin x\)
  2. \(\sin x\)
  3. \(\cos x\)
  4. \(-\cos x\)

Question 11

\(\sin(180^\circ-x)=\ ?\)
  1. \(\sin x\)
  2. \(-\sin x\)
  3. \(\cos x\)
  4. \(-\cos x\)

Question 12

\(\sin(2x)=\ ?\)
  1. \(2\sin(x)\cos(x)\)
  2. \(\sin^2(x)+\cos^2(x)\)
  3. \(2\sin^2(x)\)
  4. \(\sin(x)\cos(x)\)

Question 13

\(\sin(360^\circ-x)=\ ?\)
  1. \(-\sin x\)
  2. \(\sin x\)
  3. \(\cos x\)
  4. \(-\cos x\)

Question 14

\(\sin(A-B)=\ ?\)
  1. \(\sin A\cos B-\cos A\sin B\)
  2. \(\sin A\cos B+\cos A\sin B\)
  3. \(\cos A\cos B+\sin A\sin B\)
  4. \(\tan A-\tan B\)

Question 15

\(\sin(A+B)=\ ?\)
  1. \(\sin A\cos B+\cos A\sin B\)
  2. \(\sin A\cos B-\cos A\sin B\)
  3. \(\cos A\cos B-\sin A\sin B\)
  4. \(\tan A+\tan B\)

Question 16

\(\sin^2(x)+\cos^2(x)=\ ?\)
  1. \(1\)
  2. \(0\)
  3. \(\tan(x)\)
  4. \(\sec^2(x)\)

Question 17

\(\tan(180^\circ-x)=\ ?\)
  1. \(-\tan x\)
  2. \(\tan x\)
  3. \(\cot x\)
  4. \(-\cot x\)

Question 18

\(\tan(2x)=\ ?\)
  1. \(\frac{2\tan(x)}{1-\tan^2(x)}\)
  2. \(\frac{2\tan(x)}{1+\tan^2(x)}\)
  3. \(2\tan^2(x)\)
  4. \(\frac{\tan(x)}{2}\)

Question 19

\(\tan(A-B)=\ ?\)
  1. \(\frac{\tan A-\tan B}{1+\tan A\tan B}\)
  2. \(\frac{\tan A-\tan B}{1-\tan A\tan B}\)
  3. \(\tan A-\tan B\)
  4. \(\frac{\tan A+\tan B}{1+\tan A\tan B}\)

Question 20

\(\tan(A+B)=\ ?\)
  1. \(\frac{\tan A+\tan B}{1-\tan A\tan B}\)
  2. \(\frac{\tan A+\tan B}{1+\tan A\tan B}\)
  3. \(\tan A+\tan B\)
  4. \(\frac{\tan A-\tan B}{1-\tan A\tan B}\)

Question 21

\(\tan(x+180^\circ)=\ ?\)
  1. \(\tan x\)
  2. \(-\tan x\)
  3. \(\cot x\)
  4. \(-\cot x\)

Question 22

\(1+\cot^2(x)=\ ?\)
  1. \(\operatorname{cosec}^2(x)\)
  2. \(\sec^2(x)\)
  3. \(\cos^2(x)\)
  4. \(\tan^2(x)\)

Question 23

\(1+\tan^2(x)=\ ?\)
  1. \(\sec^2(x)\)
  2. \(\operatorname{cosec}^2(x)\)
  3. \(\cos^2(x)\)
  4. \(\sin^2(x)\)

Question 24

\(\cos(90^\circ-x)=\ ?\)
  1. \(\sin x\)
  2. \(\cos x\)
  3. \(-\sin x\)
  4. \(-\cos x\)

Question 25

\(\sin(90^\circ-x)=\ ?\)
  1. \(\cos x\)
  2. \(\sin x\)
  3. \(-\cos x\)
  4. \(-\sin x\)

Question 26

\(\tan(90^\circ-x)=\ ?\)
  1. \(\cot x\)
  2. \(\tan x\)
  3. \(-\cot x\)
  4. \(-\tan x\)

Question 27

\(\sin(3x)=\ ?\)
  1. \(3\sin x-4\sin^3x\)
  2. \(3\sin x+4\sin^3x\)
  3. \(4\sin^3x-3\sin x\)
  4. \(\sin^3x\)

Question 28

\(\cos(3x)=\ ?\)
  1. \(4\cos^3x-3\cos x\)
  2. \(4\cos^3x+3\cos x\)
  3. \(3\cos x-4\cos^3x\)
  4. \(\cos^3x\)

Question 29

\(\sin^2x=\ ?\)
  1. \(\frac{1-\cos(2x)}{2}\)
  2. \(\frac{1+\cos(2x)}{2}\)
  3. \(1-\cos(2x)\)
  4. \(\frac{1-\cos x}{2}\)

Question 30

\(\cos^2x=\ ?\)
  1. \(\frac{1+\cos(2x)}{2}\)
  2. \(\frac{1-\cos(2x)}{2}\)
  3. \(1+\cos(2x)\)
  4. \(\frac{1+\cos x}{2}\)

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Review Trig Identities questions for Maths, with correct answers shown and coverage across \cos(180^\circ-x)=\; \cos(360^\circ-x)=\; \operatorname{sec}x=\.

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