English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

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. 

If sinθ – cosθ = 0, then the value of (sin⁴θ + cos⁴θ) is ______.

sin(45° + θ) – cos(45° – θ) is equal to ______.

If cosA + cos²A = 1, then sin²A + sin⁴A = 1.

(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec²θ.

The value of 2sinθ can be `a + 1/a`, where a is a positive number, and a ≠ 1.

Prove the following:

(sin α + cos α)(tan α + cot α) = sec α + cosec α

If `sqrt(3) tan θ` = 1, then find the value of sin²θ – cos²θ.

Simplify (1 + tan²θ)(1 – sinθ)(1 + sinθ)