Math problems and answers will help you to find solutions based on math problems of all grades. We engage you to practice the topics in your curriculum. We also provide with the answers of this questions. These solutions are step by step and detailed. So if you are stuck at any point, you can refer to the answers and get it cleared.

## How to Find Answers to Math Problems

- Linear equations
- Simultaneous equations
- Quadratic equations
- Binomial Theorem
- Function
- Exponential and Logarithmic equations
- Graphing functions
- Quadratic functions
- Third degree polynomials
- Radical equations
- Trigonometry
- Geometry
- Progressions

Solved Problems: -

**Example 1: -**

If A + B = 45

^{0}, Prove that (1+ tan A)(1+ tan B) = 2.

**Solution: -**

Given A + B = 45

Then tan (A + B) = tan 45 = 1

We know that

That is = 1

Cross multiplying, we get

tan A + tan B = 1 - tan A tan B

Therefore tan A + tan B + tan A tan B = 1

Adding 1 on both sides, we get

1 + tan A + tan B + tan A tan B = 2

Grouping the first two and last two terms, we get

(1+ tan A) + tan B ( 1 + tan A) =2

Taking 1 + tan A common, we get

**(1+ tan A) ( 1+ tan B) =2**

**Hence Proved.**

Example 2: -

Find the equation of the circle passing through (0, 5) and (2, 1) and has its center on the line x + y = 1

Solution: -

Let the required equation of the circle be x

^{2}+ y

^{2}+ 2gx + 2fy + c = 0...(1)

Since (1) passes through (0,5) and (2,1), we get

25 + 10f + c = 0 and 4 + 1 + 4g + 2f + c =0

That is 10f + c = -25...(2)

4g +2f + c = -5...(3)

Since the centre (-g, -f) lies on x+ y =1, -g - f =1...(4)

Now we solve the three equations. For this,

subtract (2) from (3)

4g - 8f = 20...(5)

Dividing equation (5) by 4 we get

g - 2f = 5...(6)

Adding (4) and (6), we get

-3f = 6

f = -2

substituting in (6), we get

g - 2(-2) = 5

g + 4 = 5

g = 1

Substituting f in (2), we get

10(-2) + c = -25

-20 + c = -25

c = -5

**Therefore the required equation is x**

^{2}+ y^{2}+ 2x -4y - 5 = 0**Example 3: -**

The sum of 3 terms in Geometric Progression is 21 and their product is 216. Find the terms.

**Solution: -**

Let the three terms of the Geometric Progression be a/r, a , ar

Given sum of 3 terms in Geometric Progression is 21

That is a/r + a + ar = 21...(1)

Also their product is 216

So a/r x a x ar = 216

a

^{3}= 216

That is a = 6

Substituting in (1) we get

6/r + 6 + 6r = 21

That is 6/r + 6r = 15

(6+ 6r

^{2})/r = 15

Cross multiplying

6r

^{2}+ 6 = 15 r

Subtracting 15r on both sides, we get

6r

^{2}-15r + 6 = 0

Dividing the whole equation by 3, we get

2r

^{2 }- 5r + 2 = 0

We split the mid term

we get2r

^{2 }- 4r - r + 2 = 0

2r (r - 2) -(r - 2) = 0

(2r - 1)(r - 2) = 0

r = 1/2 or 2

when r = 1/2 and a = 6, the terms in Geometric Progression are 3, 6 and 12

when r = 2 and a = 6, the terms in Geometric Progression are 12, 6 and 3

when r = 1/2 and a = 6, the terms in Geometric Progression are 3, 6 and 12

when r = 2 and a = 6, the terms in Geometric Progression are 12, 6 and 3