English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

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 ______.

If 4 tanβ = 3, then `(4sinbeta-3cosbeta)/(4sinbeta+3cosbeta)=` ______.

If tan α + cot α = 2, then tan²⁰α + cot²⁰α = ______.

If 1 + sin²α = 3 sinα cosα, then values of cot α are ______.

The value of tan A + sin A = M and tan A - sin A = N.

The value of `("M"^2 - "N"^2) /("MN")^0.5`

The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.

Given that sin θ = `a/b`, then cos θ is equal to ______.

If cos (α + β) = 0, then sin (α – β) can be reduced to ______.

If cos 9α = sinα and 9α < 90°, then the value of tan5α is ______.