# CBSE Class 10-Mathematics: Chapter – 8 Introduction to Trigonometry Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 18**:

An army contingent of members is to march behind an army band of members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

**Answer**:

We have to find the to find the maximum number of columns in which they can march.

To find the , we can use Euclid՚s algorithm.

The is .

Therefore, they can march in 8 columns each.

**Question 19**:

Use Euclid՚s division lemma to show that the square of any positive integer is either of form for some integer *m*.

[Hint: Let be any positive integer then it is of the form . Now square each of these and show that they can be rewritten in the form or .]

**Answer**

Let be any positive integer and .

Then for some integer

And because

Therefore,

Or,

Where , and are some positive integers

Hence, it can be said that the square of any positive integer is either of the form or .

## 3 Mark Questions

**Question 1**:

Given calculate all other trigonometric ratios.

**Answer**:

Consider a triangle ABC in which

Let

Then, using Pythagoras theorem,