Science (English Medium) Class 11 - CBSE Question Bank Solutions

If \[\cos A = - \frac{12}{13}\text{ and }\cot B = \frac{24}{7}\], where A lies in the second quadrant and B in the third quadrant, find the values of the following:
sin (A + B)

If \[\cos A = - \frac{12}{13}\text{ and }\cot B = \frac{24}{7}\], where A lies in the second quadrant and B in the third quadrant, find the values of the following:
cos (A + B)

If \[\cos A = - \frac{12}{13}\text{ and }\cot B = \frac{24}{7}\], where A lies in the second quadrant and B in the third quadrant, find the values of the following:
tan (A + B)

Prove that:
\[\frac{7\pi}{12} + \cos\frac{\pi}{12} = \sin\frac{5\pi}{12} - \sin\frac{\pi}{12}\]

Prove that
\[\frac{\tan A + \tan B}{\tan A - \tan B} = \frac{\sin \left( A + B \right)}{\sin \left( A - B \right)}\]

Prove that

Prove that

Prove that

Show that one of the following progression is a G.P. Also, find the common ratio in case:

4, −2, 1, −1/2, ...

Show that one of the following progression is a G.P. Also, find the common ratio in case:

−2/3, −6, −54, ...

Show that one of the following progression is a G.P. Also, find the common ratio in case:

\[a, \frac{3 a^2}{4}, \frac{9 a^3}{16}, . . .\]

Show that one of the following progression is a G.P. Also, find the common ratio in case:1/2, 1/3, 2/9, 4/27, ...

Prove that:

Prove that:

Prove that:

Show that the sequence <a_n>, defined by a_n = \[\frac{2}{3^n}\], n ϵ N is a G.P.

Prove that \[\frac{\tan 69^\circ + \tan 66^\circ}{1 - \tan 69^\circ \tan 66^\circ} = - 1\].

Find:
the ninth term of the G.P. 1, 4, 16, 64, ...

Find:

the 10^th term of the G.P.

\[- \frac{3}{4}, \frac{1}{2}, - \frac{1}{3}, \frac{2}{9}, . . .\]

Find :

the 8^th term of the G.P. 0.3, 0.06, 0.012, ...