Question 1: Prove that:
ANSWER : L.H.S.
= 0 = R.H.S
Question 2: Prove that: (sin 3x + sin x) sin x +(cos 3x – cos x) cos x = 0
ANSWER : L.H.S.
= (sin 3x + sin x) sin x + (cos 3x – cos x) cos x
= RH.S.
Question 3: Prove that:
ANSWER : L.H.S. =
Question 4: Prove that:
ANSWER : L.H.S. =
Question 5: Prove that:
ANSWER : It is known that .
∴L.H.S. =
Question 6: Prove that:
ANSWER : It is known that
.
L.H.S. =
= tan 6x
= R.H.S.
Question 7: Prove that:
ANSWER : L.H.S. =
Question 8: , x in quadrant II
ANSWER : Here, x is in quadrant II.
i.e.,
Therefore, are all positive.
As x is in quadrant II, cosx is negative.
∴
Thus, the respective values of are .
Question 9: Find for , x in quadrant III
ANSWER : Here, x is in quadrant III.
Therefore, and are negative, whereas is positive.
Now,
Thus, the respective values of are
.
Question 10: Find for , x in quadrant II
ANSWER : Here, x is in quadrant II.
Therefore, , and are all positive.
[cosx is negative in quadrant II]
Thus, the respective values of are .
209 videos|443 docs|143 tests
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1. What are trigonometric functions? |
2. How are trigonometric functions used in real-life applications? |
3. What is the unit circle and how is it related to trigonometric functions? |
4. How can I find the values of trigonometric functions for specific angles? |
5. Are there any important identities or formulas related to trigonometric functions? |
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