English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

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.

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 ______.

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

If cos 9α = sin α and 9α < 90°, then the value of tan 5α 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.