PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

Equation of the circle through origin which cuts intercepts of length a and b on axes is

If the circles x² + y² + 2ax + c = 0 and x² + y² + 2by + c = 0 touch each other, then

Prove that:

Prove that:

Prove that: 

Show that :

Show that :

Prove that:
cos 10° cos 30° cos 50° cos 70° = \[\frac{3}{16}\]

Prove that:
cos 40° cos 80° cos 160° = \[- \frac{1}{8}\]

Prove that:
 sin 20° sin 40° sin 80° = \[\frac{\sqrt{3}}{8}\]

Prove that:
cos 20° cos 40° cos 80° = \[\frac{1}{8}\]

Prove that:
tan 20° tan 40° tan 60° tan 80° = 3

Prove that tan 20° tan 30° tan 40° tan 80° = 1.

Prove that:
sin 10° sin 50° sin 60° sin 70° = \[\frac{\sqrt{3}}{16}\]

Prove that:
 sin 20° sin 40° sin 60° sin 80° = \[\frac{3}{16}\]

Show that:
sin A sin (B − C) + sin B sin (C − A) + sin C sin (A − B) = 0

Show that:
sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0

Prove that 
\[\tan x \tan \left( \frac{\pi}{3} - x \right) \tan \left( \frac{\pi}{3} + x \right) = \tan 3x\]

If α + β = \[\frac{\pi}{2}\], show that the maximum value of cos α cos β is \[\frac{1}{2}\].