Question 24:
Prove that cos 4x = 1−8sin2 x cos2 x
Answer
L.H.S. = cos 4x
= cos 2(2x)
= 1 −2 sin2 2x [cos 2A = 1 − 2 sin2 A]
= 1 − 2(2 sin x cos x)2 [sin2A = 2sin A cosA]
= 1 − 8 sin2x cos2x
= R.H.S.
Exams Question Papers General Knowledge Election Directory
Question 24:
Prove that cos 4x = 1−8sin2 x cos2 x
Answer
L.H.S. = cos 4x
= cos 2(2x)
= 1 −2 sin2 2x [cos 2A = 1 − 2 sin2 A]
= 1 − 2(2 sin x cos x)2 [sin2A = 2sin A cosA]
= 1 − 8 sin2x cos2x
= R.H.S.
Question 23:
Answer
Question 22:
Prove that cot x cot 2x − cot 2x cot 3x − cot 3x cot x = 1
Answer
Question 21:
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Question 20:
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Question 19:
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Question 18:
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Question 17:
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Question 16:
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Question 15:
Prove that cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)
Answer
Question 14:
Prove that sin 2x + 2sin 4x + sin 6x = 4cos2 x sin 4x
Answer
Question 13:
Prove that cos2 2x – cos2 6x = sin 4x sin 8x
Answer
Question 12:
Prove that sin2 6x – sin2 4x = sin 2x sin 10x
Answer
Question 11:
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Question 10:
Prove that sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x
Answer
Question 5:
Find the value of:
(i) sin 75°
(ii) tan 15°
Answer
(i) sin 75° = sin (45° + 30°)
= sin 45° cos 30° + cos 45° sin 30°
[sin (x + y) = sin x cos y + cos x sin y]
(ii) tan 15° = tan (45° − 30°)