English Medium कक्षा १० - CBSE Important Questions for Mathematics

Prove that:

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

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

If cos A = `4/5`, then the value of tan A is ______.

Show that `(cos^2(45^circ + θ) + cos^2(45^circ - θ))/(tan(60^circ + θ) tan(30^circ - θ)) = 1`

If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q(p² – 1) = 2p.

If sin A = `1/2`, then the value of sec A is ______.

`sqrt(3)` cos²A + `sqrt(3)` sin²A is equal to ______.

If sin θ + cos θ = `sqrt(2)` then tan θ + cot θ = ______.

If 5 tan β = 4, then `(5  sin β - 2 cos β)/(5 sin β + 2 cos β)` = ______.

Find an acute angle θ when `(cos θ - sin θ)/(cos θ + sin θ) = (1 - sqrt(3))/(1 + sqrt(3))`

Prove the following that:

`tan^3θ/(1 + tan^2θ) + cot^3θ/(1 + cot^2θ)` = secθ cosecθ – 2 sinθ cosθ

If θ is an acute angle of a right angled triangle, then which of the following equation is not true?

If tan θ = `x/y`, then cos θ is equal to ______.

Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?

If θ is an acute angle and sin θ = cos θ, find the value of tan² θ + cot² θ – 2.

(sec² θ – 1) (cosec² θ – 1) is equal to ______.

Evaluate 2 sec² θ + 3 cosec² θ – 2 sin θ cos θ if θ = 45°.

If sin θ – cos θ = 0, then find the value of sin⁴ θ + cos⁴ θ.

(1 – cos² A) is equal to ______.

Prove that `(1 + tan^2 A)/(1 + cot^2 A)` = sec² A – 1