English Medium इयत्ता १० - CBSE Question Bank Solutions

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 ______.

If sinA + sin²A = 1, then the value of the expression (cos²A + cos⁴A) is ______.

`sqrt((1 - cos^2theta) sec^2 theta) = tan theta` 

Prove the following:

`sintheta/(1 + cos theta) + (1 + cos theta)/sintheta` = 2cosecθ

Prove the following:

`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A

Prove the following:

`1 + (cot^2 alpha)/(1 + "cosec"  alpha)` = cosec α

If cosec θ + cot θ = p, then prove that cos θ = `(p^2 - 1)/(p^2 + 1)`

Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`

If 1 + sin²θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.

Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.

The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. Find x and y.

The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.

The angles of a cyclic quadrilateral ABCD are ∠A = (6x + 10)°, ∠B = (5x)°, ∠C = (x + y)°, ∠D = (3y – 10)°. Find x and y, and hence the values of the four angles.