CBSE Class 10-Mathematics: Chapter – 8 Introduction to Trigonometry Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)
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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