CBSE Class 10 Mathematics Trigonometry Assignment Set 15

Question. \( \sin (90^\circ - \theta) \cdot \cos \theta \) is
(a) \( 1 - \sin^2 \theta \)
(b) \( 1 - \cos^2 \theta \)
(c) \( 1 - \tan^2 \theta \)
(d) None of the options
Answer: (a) \( 1 - \sin^2 \theta \)

Question. If \( \sin (90^\circ - 3A) = \cos (5A - 10^\circ) \), the value of \( A \) is
(a) \( 15^\circ \)
(b) \( 5^\circ \)
(c) \( 10^\circ \)
(d) \( 12^\circ \)
Answer: (b) \( 5^\circ \)

Question. If \( \sec (90^\circ + 7A) = \csc (2A - 63^\circ) \) then the value of \( A \) is
(a) \( 17^\circ \)
(b) \( 27^\circ \)
(c) \( 7^\circ \)
(d) \( 37^\circ \)
Answer: (c) \( 7^\circ \)

Question. \( \sin 30^\circ \times \cos 60^\circ \times \tan 0^\circ \) is
(a) \( \frac{1}{2} \)
(b) \( \frac{1}{4} \)
(c) \( \frac{\sqrt{3}}{4} \)
(d) \( 0 \)
Answer: (d) \( 0 \)

Question. \( \sin^2 30^\circ + \cos^2 60^\circ - \tan^2 45^\circ \) is
(a) \( -\frac{1}{2} \)
(b) \( +\frac{1}{2} \)
(c) \( \frac{1}{4} \)
(d) \( -\frac{1}{4} \)
Answer: (a) \( -\frac{1}{2} \)

Question. As \( \theta \) increases, the value of \( \sin \theta \)
(a) increases
(b) decreases
(c) Constant
(d) None of the options
Answer: (a) increases

Question. As \( \theta \) increases, the value of \( \tan \theta \) is
(a) \( > 1 \)
(b) \( < 1 \)
(c) \( = 1 \)
(d) Can take any value.
Answer: (d) Can take any value.

Question. For \( A = 30^\circ \), the value of \( \sin 2A \) is
(a) \( \frac{1}{2} \)
(b) \( 1 \)
(c) \( \frac{\sqrt{3}}{2} \)
(d) \( \frac{2}{\sqrt{3}} \)
Answer: (c) \( \frac{\sqrt{3}}{2} \)

Question. For \( A = 45^\circ \), the value of \( \tan 2A \) is
(a) n.d
(b) \( 1 \)
(c) \( 2 \)
(d) \( 3 \)
Answer: (a) n.d

Question. For \( A = 30^\circ \), the value of \( 4\cos^3 A - 3\cos A \)
(a) \( 1 \)
(b) \( 0 \)
(c) \( 4 \)
(d) \( 3 \)
Answer: (b) \( 0 \)

Question. \( (\sin A + \csc A)^2 + (\cos^2 A - \cot^2 A) \) is
(a) \( 1 \)
(b) \( 3 \)
(c) \( 4 \)
(d) \( 0 \)
Answer: (c) \( 4 \)

Question. \( (\sec A - \cos A)^2 + (\sin^2 A - \tan^2 A) \) is
(a) \( 3 \)
(b) \( 2 \)
(c) \( 1 \)
(d) \( 0 \)
Answer: (d) \( 0 \)

Question. If \( \sec A + \tan A = 4 \), the value of \( (\sec A - \tan A) \) is
(a) \( \frac{1}{4} \)
(b) \( 1 \)
(c) \( 3/4 \)
(d) \( 5/4 \)
Answer: (a) \( \frac{1}{4} \)

Question. If \( \frac{1}{\sin A} - \frac{\cos A}{\sin A} = 3 \) then \( \frac{1}{\sin A} + \frac{\cos A}{\sin A} \) is
(a) \( 3 \)
(b) \( \frac{1}{3} \)
(c) \( 1 \)
(d) \( 0 \)
Answer: (b) \( \frac{1}{3} \)

Question. If \( \sin A = \frac{4}{5} \) then \( \cos A \) is
(a) \( \frac{5}{4} \)
(b) \( 1 \)
(c) \( 3/5 \)
(d) \( \frac{16}{25} \)
Answer: (c) \( 3/5 \)

Question. If \( \tan A = \frac{7}{24} \) then \( \sec A \) is
(a) \( \frac{24}{7} \)
(b) \( \frac{7}{25} \)
(c) \( \frac{24}{25} \)
(d) \( \frac{25}{24} \)
Answer: (d) \( \frac{25}{24} \)

Question. If \( \csc A - \cot A = 5 \), the value of \( \cos A \) is
(a) \( \frac{12}{13} \)
(b) \( \frac{5}{13} \)
(c) \( \frac{13}{12} \)
(d) \( \frac{13}{5} \)
Answer: (a) \( \frac{12}{13} \)

Question. The value of \( \sin 31^\circ \cos 59^\circ + \cos 31^\circ \sin 59^\circ \) is
(a) \( 0 \)
(b) \( 1 \)
(c) \( 1/2 \)
(d) \( \frac{\sqrt{3}}{2} \)
Answer: (b) \( 1 \)

Question. \( (\csc A + \cot A)(1 - \cos A) \) is
(a) \( \sin 2A \)
(b) \( \cos A \)
(c) \( \sin A \)
(d) \( \sin^2 A \)
Answer: (c) \( \sin A \)

Question. The value of \( (\sec A - \tan A)(\sec A + \tan A) \) is
(a) \( \tan A \)
(b) \( \cot A \)
(c) \( 0 \)
(d) \( 1 \)
Answer: (d) \( 1 \)