English Medium Class 10 - CBSE Question Bank Solutions

A fraction becomes `1/3` when 2 is subtracted from the numerator and it becomes `1/2` when 1 is subtracted from the denominator. Find the fraction.

Prove that :(sinθ+cosecθ)²+(cosθ+ secθ)² = 7 + tan² θ+cot² θ.

Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2. 

A fraction becomes `(1)/(3)` when 2 is subtracted from the numerator and it becomes `(1)/(2)` when 1 is subtracted from the denominator. Find the fraction.

Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`

Evaluate:
`(tan 65°)/(cot 25°)`

Express (sin 67° + cos 75°) in terms of trigonometric ratios of the angle between 0° and 45°.

Prove that (sin θ + cosec θ)² + (cos θ + sec θ)² = 7 + tan² θ + cot² θ. 

If sec θ = x + `1/(4"x"), x ≠ 0,` find (sec θ + tan θ)

Evaluate:

`(tan 65^circ)/(cot 25^circ)`

Prove that:
`sqrt(( secθ - 1)/(secθ + 1)) + sqrt((secθ + 1)/(secθ - 1)) = 2cosecθ`

Prove that:

`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`

Prove that: 2(sin⁶ θ + cos⁶ θ) – 3 (sin⁴ θ + cos⁴ θ) + 1 = 0.

A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.

There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole.

If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`

If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.

The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is ______.

If tan θ = 3, then `(4 sin theta - cos theta)/(4 sin theta + cos theta)` is equal to ______.

If 2sin²β − cos²β = 2, then β is ______.