CBSE Class 10 Mathematics Trigonometry Assignment Set 14

\(\triangle ABC\) is a right angled triangle at A. If \(AB = 5\text{ cm}\), \(BC = 13\text{ cm}\) and \(AC = 12\text{ cm}\).
Answer the following questions by selecting the correct answer from the diagram.

Question. The value of \(\sin B\)
(a) \(\frac{12}{13}\)
(b) \(\frac{5}{13}\)
(c) \(\frac{5}{12}\)
(d) \(\frac{13}{12}\)
Answer: (a) \(\frac{12}{13}\)

Question. The value of \(\tan C\)
(a) \(\frac{12}{5}\)
(b) \(\frac{5}{12}\)
(c) \(\frac{12}{13}\)
(d) \(\frac{13}{5}\)
Answer: (b) \(\frac{5}{12}\)

Question. The value of \(\sec B\)
(a) \(\frac{13}{5}\)
(b) \(\frac{12}{5}\)
(c) \(\frac{5}{13}\)
(d) \(\frac{12}{13}\)
Answer: (a) \(\frac{13}{5}\)

Question. The value of \(\sin^2 B + \sin^2 C\) is
(a) \(\frac{144}{169}\)
(b) \(\frac{25}{169}\)
(c) \(\frac{169}{25}\)
(d) \(1\)
Answer: (d) 1

Question. The value of \(\frac{\tan C}{\sec B}\)
(a) \(\frac{13}{12}\)
(b) \(\frac{25}{156}\)
(c) \(\frac{65}{60}\)
(d) \(\frac{60}{156}\)
Answer: (b) \(\frac{25}{156}\)

Question. The value of \(\sec^2 B - \tan^2 B\) is
(a) \(\frac{25}{169}\)
(b) \(1\)
(c) \(\frac{144}{169}\)
(d) \(\frac{288}{169}\)
Answer: (b) 1

Question. The value of \(\text{cosec}^2 C - \tan^2 B\) is
(a) \(\frac{169}{25}\)
(b) \(\frac{144}{25}\)
(c) \(1\)
(d) \(\frac{313}{25}\)
Answer: (c) 1

Question. The value of \(\sin^2 B + \cos^2 B\) is
(a) \(\frac{25}{169}\)
(b) \(\frac{144}{169}\)
(c) \(\frac{169}{144}\)
(d) \(1\)
Answer: (d) 1

Question. The value of \(\frac{\sin B}{\cos C} \times \frac{\sin C}{\cos B}\) is
(a) \(1\)
(b) \(\frac{25}{169}\)
(c) \(\frac{144}{169}\)
(d) \(\frac{60}{169}\)
Answer: (a) 1

Question. The value of \(\frac{\text{cosec}^2 C - \text{cot}^2 C}{\sec^2 B - \tan^2 B}\)
(a) \(\frac{25}{144}\)
(b) \(1\)
(c) \(\frac{169}{144}\)
(d) \(\frac{144}{169}\)
Answer: (b) 1

Question. The value of \(\sin 60^\circ\) is
(a) \(\frac{1}{\sqrt{2}}\)
(b) \(\frac{1}{2}\)
(c) \(\frac{\sqrt{3}}{2}\)
(d) \(1\)
Answer: (c) \(\frac{\sqrt{3}}{2}\)

Question. The value of \(\tan 60^\circ\) is
(a) \(1\)
(b) \(\frac{\sqrt{3}}{2}\)
(c) \(\frac{2}{\sqrt{3}}\)
(d) \(\sqrt{3}\)
Answer: (d) \(\sqrt{3}\)

Question. The value of \(\cos 0^\circ\) is
(a) \(1\)
(b) \(0\)
(c) \(\frac{1}{2}\)
(d) not defined
Answer: (a) 1

Question. The value of \(\cot 45^\circ\) is
(a) \(\frac{1}{\sqrt{3}}\)
(b) \(1\)
(c) \(\sqrt{3}\)
(d) Undefined
Answer: (b) 1

Question. The value of \(\cot 0^\circ\) is
(a) \(0\)
(b) \(1\)
(c) Undefined
(d) \(\sqrt{3}\)
Answer: (c) Undefined

Question. The maximum value of \(\sin \theta\) is
(a) \(0\)
(b) \(\sqrt{3}\)
(c) \(\frac{1}{\sqrt{3}}\)
(d) \(1\)
Answer: (d) 1

Question. The minimum value of \(\cos \theta\) is
(a) \(-1\)
(b) \(+1\)
(c) \(0\)
(d) None of the options
Answer: (a) \(-1\)

Question. \(\sin(90^\circ - \theta)\) is the same as
(a) \(\cot \theta \cos \theta\)
(b) \(\cot \theta \sin \theta\)
(c) \(\cot \theta \text{cosec } \theta\)
(d) None of the options
Answer: (b) \(\cot \theta \sin \theta\)

Question. \(\tan(60^\circ - \theta)\) is the same as,
(a) \(\cot(60^\circ + \theta)\)
(b) \(\cot(60^\circ - \theta)\)
(c) \(\cot(30^\circ + \theta)\)
(d) \(\cot(30^\circ - \theta)\)
Answer: (c) \(\cot(30^\circ + \theta)\)

Question. \(\sin 65^\circ \times \sec 25^\circ\) is
(a) \(\sin^2 65^\circ\)
(b) \(\sec^2 25^\circ\)
(c) \(\tan^2 25^\circ\)
(d) \(\sin^2 90^\circ\)
Answer: (d) \(\sin^2 90^\circ\)