English Medium Class 10 - CBSE Question Bank Solutions

If 5x = sec θ and \[\frac{5}{x} = \tan \theta\]find the value of \[5\left( x^2 - \frac{1}{x^2} \right)\] 

If cosec θ = 2x and \[5\left( x^2 - \frac{1}{x^2} \right)\] \[2\left( x^2 - \frac{1}{x^2} \right)\] 

 Write True' or False' and justify your answer  the following : 

The value of  \[\sin \theta\] is \[x + \frac{1}{x}\] where 'x'  is a positive real number . 

Write True' or False' and justify your answer the following: 

\[ \cos \theta = \frac{a^2 + b^2}{2ab}\]where a and b are two distinct numbers such that ab > 0.

 Write True' or False' and justify your answer  the following : 

The value of  \[\cos^2 23 - \sin^2 67\]  is positive . 

 Write True' or False' and justify your answer the following :

The value of the expression \[\sin {80}^° - \cos {80}^°\] 

 Write True' or False' and justify your answer  the following : 

The value of sin θ+cos θ is always greater than 1 .

If sec θ + tan θ = x, then sec θ =

If \[sec\theta + tan\theta = x\] then \[tan\theta =\] 

\[\frac{x^2 - 1}{2x}\] is equal to 

The value of \[\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}}\]

sec⁴ A − sec² A is equal to

cos⁴ A − sin⁴ A is equal to ______.

\[\frac{\sin \theta}{1 + \cos \theta}\]is equal to 

\[\frac{1 - \sin \theta}{\cos \theta}\] is equal to

The value of (1 + cot θ − cosec θ) (1 + tan θ + sec θ) is 

\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to 

(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to

If x = a cos θ and y = b sin θ, then b²x² + a²y² =

If x = a sec θ and y = b tan θ, then b²x² − a²y² =