English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

If 2sin²θ – cos²θ = 2, then find the value of θ.

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

Show that tan⁴θ + tan²θ = sec⁴θ – sec²θ.

If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.

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

If a sinθ + b cosθ = c, then prove that a cosθ – b sinθ = `sqrt(a^2 + b^2 - c^2)`.

Prove that `(1 + sec theta - tan theta)/(1 + sec theta + tan theta) = (1 - sin theta)/cos theta`

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

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

Prove the following that:

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

A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.

`(cos^2 θ)/(sin^2 θ) - 1/(sin^2 θ)`, in simplified form, is ______.

Proved that `(1 + secA)/secA = (sin^2A)/(1 - cos A)`.

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

sec θ when expressed in term of cot θ, is equal to ______.

Read the following passage:

Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per student. School 'P' decided to award a total of ₹ 9,500 for the two games to 5 and 4 Students respectively; while school 'Q' decided to award ₹ 7,370 for the two games to 4 and 3 students respectively.

Based on the above information, answer the following questions:

1. Represent the following information algebraically (in terms of x and y).
2. (a) What is the prize amount for hockey?
   OR
   (b) Prize amount on which game is more and by how much?
3. What will be the total prize amount if there are 2 students each from two games?

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

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

(1 – cos² A) is equal to ______.

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