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If cos θ + sin θ = √2 cos θ, prove that cos θ – sin θ = √2 sin θ.

Given,cos θ + sin θ = √2 cos θSquaring on both sides,(cos θ + sin θ)2 = (√2 cos θ)2cos2θ +... View Article

What is ordinate in maths?

The y-coordinate of a point is called the ordinate. It is the perpendicular distance from the x-axis measured along the y-axis. Also, its value... View Article

___ is the factor of every number.

1 is the factor of every number.Every number other than 1, has at least two factors.... View Article

Find the LCM of 25 and 40 by the prime factorization method.

Prime factorization of 25 is: 25 = 5 × 5Prime factorization of 40 is: 40 = 2 × 2 × 2 × 5LCM(25, 40) = 2 × 2 ×... View Article

Express 0.(001) bar in p/q form.

Let = x So, x = 0.001001.....(i) Multiply by 1000 on both sides, 1000x = 1.001001.....(ii) Subtracting (i) from (ii), 1000x - x = 1.001001... -... View Article

The value of cos 540° is

Let us write the angle 540° as a sum or difference using the period of cos function.cos 540° = cos(180° + 360°)= cos 180°=... View Article

Find the cube root of 27000 by prime factorization method.

The first step in finding the cube root of 27000 by prime factorization method is to write 27000 as the product of its prime numbers. i.e. 27000... View Article

Find the roots of x + 1/x = 3; x ≠ 0.

Given,x + 1/x = 3; x ≠ 0(x2 + 1)/x = 3x2 + 1 = 3xx2 - 3x + 1 = 0Comparing with the standard form ax2 + bx + c = 0,a = 1, b = -3, c = 1Using... View Article

Write first five multiples of given numbers 5, 8, 9.

The first five multiples of 5 are: 5 × 1 = 5 5 × 2 = 10 5 × 3 = 15 5 × 4 = 20 5 × 5 = 25 Hence, the first five multiples of 5 are 5, 10, 15, 20... View Article

The sum of first five multiples of 3 is

The first five multiples of 3 are: 3, 6, 9, 12, 15Sum = 3 + 6 + 9 + 12 + 15 = 45Hence, the sum of first five multiples of 3 is... View Article

Use Euclids division algorithm to find the HCF of 196 and 38220.

38220 > 196 Using Euclid's division algorithm, 38220 = 196 × 195 + 0 Here, the remainder is 0. Therefore, the HCF of 196 and 38220 is 196.... View Article

Add 3x + 11 and 7x – 5.

Addition of 3x + 11 and 7x - 5 can be done as follows.(3x + 11) + (7x - 5)Let us group the like terms. = (3x + 7x) + (11 - 5)= 10x + 6... View Article

Find the square root of 125 by long divison method.

The long division method is the most agile method to find the square root of 125. In this method, we pair the digits starting from the right-hand... View Article

What are the factors of 37?

The factors of 37 are 1 and 37. As we know, 37 is a prime number so it has only two factors, i.e. one and the number itself.... View Article

The product of x + 3 and 2x – 1 is

(x + 3)(2x - 1) = x(2x) + 3(2x) + x(-1) + 3(-1) = 2x2 + 6x - x - 3 = 2x2 + 5x - 3 Therefore, the product of x + 3 and 2x - 1 is 2x2 + 5x - 3.... View Article

The square of 43 ends with the digit ____ .

(a) 9(b) 3(c) 4(d) 6Correct option: (a) 9432 = 43 × 43 = 1849Therefore, the square of 43 ends with the digit 9.... View Article

If 1 m is equal to 39.37 inch, how many inches will be equal to 16 m?

Given,1 m = 39.37 inches16 m = ?So,16 m = 16 × 39.97 inches= 629.92 inchesTherefore, 629.92 inches will be equal to 16 m.... View Article

Find the 10th term of the AP: 2, 7, 12,…

Given AP: 2, 7, 12,... First term = a = 2 Common difference = d = 7 - 2 = 5 We know that nth term of an AP is an = a + (n - 1)d 10th term = a10 =... View Article

Find the value of a and b in the following: (5 + 2√3)/(7 + 4√3) = a – b√3

Given,(5 + 2√3)/(7 + 4√3) = a - b√3 By rationalizing the denominator in LHS,(5 + 2√3)/(7 + 4√3) = a - b√3 [(5... View Article

Find the square root of 1369 by long division method.

The long division method is the most agile method to find the square root of 1369. In this method, we pair the digits starting from the... View Article