Taking A = 30°, verify that
(i) cos4 A – sin4 A = cos 2A
(ii) 4cos A cos (60° – A) cos (60° + A) = cos 3 A.
Answer :
(i) cos4 A – sin4 A = cos 2A
Let’s take A = 30°
so,
we have
L.H.S.= cos4 A – sin4 A = cos4 30° – sin4 30°
R.H.S. = cos 2A = cos 2(30o) = ½
Therefore, L.H.S. = R.H.S. hence verified.
(ii) 4 cos A cos (60°- A) cos (60° + A) = cos 3 A
Let’s take A = 30°
L.H.S. = 4 cos A cos (60° – A) cos (60° + A)
= 4 cos 30° cos (60° – 30°) cos (60° + 30°)
= 4 cos 30° cos 30° cos 90°
= 4 × (√3/2) × (√3/2) × 0
= 0
R.H.S. = cos 3A
= cos (3 × 30°) = cos 90° = 0
Therefore, L.H.S. = R.H.S.
Hence proofed
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