PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

Find the value of the other five trigonometric functions 

\[\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + . . . + \frac{1}{2^n} = 1 - \frac{1}{2^n}\]

Find the value of the other five trigonometric functions 
\[\tan x = \frac{3}{4},\] x in quadrant III

Find the value of the other five trigonometric functions
\[\sin x = \frac{3}{5},\] x in quadrant I

1² + 3² + 5² + ... + (2n − 1)² = \[\frac{1}{3}n(4 n^2 - 1)\]

If sin \[x = \frac{12}{13}\] and x lies in the second quadrant, find the value of sec x + tan x.

If sin\[x = \frac{3}{5}, \tan y = \frac{1}{2}\text{ and }\frac{\pi}{2} < x < \pi < y < \frac{3\pi}{2},\]  find the value of 8 tan \[x - \sqrt{5} \sec y\]

a + ar + ar² + ... + arⁿ⁻¹ =  \[a\left( \frac{r^n - 1}{r - 1} \right), r \neq 1\]

a + (a + d) + (a + 2d) + ... (a + (n − 1) d) = \[\frac{n}{2}\left[ 2a + (n - 1)d \right]\]

If \[\cos x = - \frac{3}{5}\text{ and }\pi < x < \frac{3\pi}{2}\] find the values of other five trigonometric functions and hence evaluate \[\frac{cosec x + \cot x}{\sec x - \tan x}\]

5²ⁿ −1 is divisible by 24 for all n ∈ N.

Find the value of the following trigonometric ratio:

Find the value of the following trigonometric ratio:
sin 17π

Find the value of the following trigonometric ratio:
\[\tan\frac{11\pi}{6}\]

Find the value of the following trigonometric ratio:

Find the value of the following trigonometric ratio:
\[\tan \frac{7\pi}{4}\]