English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

What is the value of (1 + tan² θ) (1 − sin θ) (1 + sin θ)?

If \[\cos A = \frac{7}{25}\]  find the value of tan A + cot A. 

If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot² θ + 2. 

If \[\cos \theta = \frac{3}{4}\] then find the value of 9 tan² θ + 9. 

If sec² θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.

If sin² θ cos² θ (1 + tan² θ) (1 + cot² θ) = λ, then find the value of λ. 

If cosec² θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ. 

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 in 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 in 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 in 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 ______.