Trigonometry Formulas Quiz Part 2

Question 1 of 25

1. Question

If $A+B=90^\circ$, then what is the relation between $A$ and $B$?

They are supplementary
They are complementary
They are equal
They are opposite

Question 2 of 25

2. Question

Which relation is correct between $\sin A$ and $\cos B$?

$\sin A = \cos B$
$\sin A = \sin B$
$\cos A = \cos B$
$\cos A = \sin B$

Question 3 of 25

3. Question

If $\tan A = \cot B$, then which of the following is true?

$\tan A \tan B = 1$
$\tan A + \tan B = 1$
$\cot A + \cot B = 1$
$\tan A = \tan B$

Question 4 of 25

4. Question

Which relation is correct between $\sec A$ and $\csc B$?

$\sec A + \csc B = 1$
$\cos A \csc B = 1$
$\sec A \csc B = 1$
$\cos A + \csc B = 1$

Question 5 of 25

5. Question

What is the value of $\tan 31^\circ \times \tan 59^\circ$?

$0$
$1$
$\sqrt{3}$
$\dfrac{1}{\sqrt{3}}$

Question 6 of 25

6. Question

Which identity is correct?

$\sin^2 A + \sin^2 B = 1$
$\sin^2 A + \sin^2 (90^\circ - A) = 1$
$\sin^2 A + \cos^2 B = 1$
$\cos^2 A + \sin^2 B = 1$

Question 7 of 25

7. Question

Which of the following is true about $\cos^2 A + \cos^2 B$?

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

Question 8 of 25

8. Question

Which of the following is correct regarding the triple angle identity for tangent?

$\tan 3A = \frac{3 \tan A + \tan^3 A}{1 - 3 \tan^2 A}$
$\tan 3A = \frac{3 \tan A - \tan^3 A}{1 - 3 \tan^2 A}$
$\tan 3A = \frac{\tan A - 3 \tan^3 A}{1 + 3 \tan^2 A}$
$\tan 3A = \frac{\tan^3 A - 3 \tan A}{1 - \tan^2 A}$

Question 9 of 25

9. Question

Which formula is equivalent to $\cos^2 A + \cos^2 B = 1$?

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

Question 10 of 25

10. Question

What is the simplified form of $\sin 18^\circ$ using surds?

$\frac{\sqrt{5} + 1}{4}$
$\frac{\sqrt{5} - 1}{4}$
$\frac{\sqrt{10 + 2\sqrt{5}}}{4}$
$\frac{\sqrt{10 - 2\sqrt{5}}}{4}$

Question 11 of 25

11. Question

Which identity is correct for $\cos 75^\circ$?

$\frac{\sqrt{3} - 1}{2\sqrt{2}}$
$\frac{\sqrt{3} + 1}{2\sqrt{2}}$
$1$
$\frac{1}{\sqrt{2}}$

Question 12 of 25

12. Question

What is the value of $\tan 15^\circ + \tan 75^\circ$?

$2$
$2\sqrt{3}$
$4$
$2 + \sqrt{3}$

Question 13 of 25

13. Question

Which identity gives the correct result of $\cos \theta \cos 2\theta \cos 2^2\theta \dots \cos 2^n\theta$?

$\frac{\sin 2^n \theta}{2^n \sin \theta}$
$\frac{\sin 2^{n+1} \theta}{2^{n+1} \sin \theta}$
$\frac{\cos n\theta}{n \cos \theta}$
$\frac{\cos n\theta}{2^n \sin \theta}$

Question 14 of 25

14. Question

If $A + B = 90^\circ$, which of the following is true?

$\sin A = \sin B$
$\sin A = \cos B$
$\tan A = \tan B$
$\tan A = \cot B$

Question 15 of 25

15. Question

Which identity is equivalent to $\tan A \tan B = 1$?

$A + B = 90^\circ$
$A - B = 90^\circ$
$A + B = 180^\circ$
$A - B = 180^\circ$

Question 16 of 25

16. Question

What is the value of $\tan 31^\circ \cdot \tan 59^\circ$?

$0$
$1$
$\sqrt{3}$
$2$

Question 17 of 25

17. Question

If $\tan A + \tan B + \tan C = \tan A \tan B \tan C$, then what is $A + B + C$?

$60^\circ$
$90^\circ$
$180^\circ$
$120^\circ$

Question 18 of 25

18. Question

Which identity is equivalent to $\cos^2 A + \cos^2(60^\circ – \theta) + \cos^2(60^\circ + \theta)$?

$1$
$2$
$3$
$\frac{3}{2}$

Question 19 of 25

19. Question

If $\tan(A + B) = \frac{1 + \tan A \tan B}{\tan A – \tan B}$, what must $A + B$ be?

$60^\circ$
$30^\circ$
$45^\circ$
$90^\circ$

Question 20 of 25

20. Question

The value of $\tan 45^\circ$ using identity $\frac{1 – \tan \theta}{1 + \tan \theta}$ equals:

$0$
$1$
$\infty$
$-1$

Question 21 of 25

21. Question

What is $\sin \theta \sin(60^\circ – \theta) \sin(60^\circ + \theta)$ equal to?

$\frac{1}{4} \sin 3\theta$
$\sin 3\theta$
$\frac{1}{2} \sin 3\theta$
$\frac{3}{4} \sin 3\theta$

Question 22 of 25

22. Question

Which expression is correct for $\cos^2 A + \cos^2(120^\circ – A) + \cos^2(120^\circ + A)$?

$2$
$3$
$1$
$\frac{3}{2}$

Question 23 of 25

23. Question

The identity $\cot \theta – \cot(60^\circ + \theta) + \cot(60^\circ – \theta)$ simplifies to:

$\cot 30^\circ$
$0$
$2$
$3\cot \theta$

Question 24 of 25

24. Question

What is $\tan 4\theta = \frac{4 \tan \theta (1 – \tan^2 \theta)}{1 – 6 \tan^2 \theta + \tan^4 \theta}$ known as?

Double angle identity
Triple angle identity
Quadruple angle identity
Product-to-sum identity

Question 25 of 25

25. Question

If $\tan(A + B + C) = \frac{\tan A + \tan B + \tan C – \tan A \tan B \tan C}{1 – \tan A \tan B – \tan B \tan C – \tan C \tan A}$, then $A + B + C$ must be:

$60^\circ$
$90^\circ$
$180^\circ$
Not determinable

Quiz	Trigonometry Formulas
Subject	Mathematics
Part	2
Questions	25