English Medium Class 10 - CBSE Important Questions

`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

(3 sin² 30° – 4 cos² 60°) is equal to ______.

In a right triangle PQR, right angled at Q. If tan P = `sqrt(3)`, then evaluate 2 sin P cos P.

In ΔBC, right angled at C, if tan A = `8/7`, then the value of cot B is ______.

If the total surface area of a solid hemisphere is 462 cm2 , find its volume.[Take π=22/7]

The largest possible sphere is carved out of a wooden solid cube of side 7 em. Find the volume of the wood left. (Use\[\pi = \frac{22}{7}\]).

Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/h. How much area will it irrigate in 10 minutes, if 8 cm of standing water is needed for irrigation?