# CBSE Class 10-Mathematics: Chapter – 8 Introduction to Trigonometry Part 7 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 15**:

Write the other trigonometric ratios of A in terms of .

**Answer**:

For ,

By using identity,

For ,

For ,

By using identity

For

**Question16**:

Evaluate:

(i)

(ii)

**Answer**:

(i)

(ii)

**Question17**:

Show that any positive odd integer is of the form , where *q* is some integer.

**Answer**:

Let be any positive integer and . Then, by Euclid՚s algorithm,

for some integer , and because .

Therefore, or or or or

Also, , where is a positive integer

, where is an integer

6*q* + 5 = (6*q* + 4) + 1 = 2 (3*q* + 2) + 1 = 2*k*_{3} + 1, where *k*_{3} is an integer

Clearly, are of the form, where *k* is an integer.

Therefore, 6*q* + 1,6*q* + 3,6*q* + 5 are not exactly divisible by . Hence, these expressions of numbers are odd numbers.

And therefore, any odd integer can be expressed in the form ,

Or