CBSE Class 10-Mathematics: Chapter –8 Introduction to Trigonometry Part 7

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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

6q + 5 = (6q + 4) + 1 = 2 (3q + 2) + 1 = 2k₃ + 1, where k₃ is an integer

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

Therefore, 6q + 1, 6q + 3, 6q + 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