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प्रश्न
cos4 A − sin4 A is equal to ______.
(cos4 A − sin4 A) on simplification, gives
विकल्प
2 cos2 A + 1
2 cos2 A − 1
2 sin2 A − 1
2 sin2 A + 1
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उत्तर
cos4 A − sin4 A is equal to 2 cos2 A − 1.
Explanation:
The given expression is cos4 A − sin4 A.
Factorising the given expression, we have
cos4 A − sin4 A = [(cos2 A)2 − (sin2 A)2]
= (cos2 A + sin2 A) × (cos2 A − sin2 A) ...[∵ (a2 − b2) = (a + b)(a − b)]
= cos2 A − sin2 A ...[∵ sin2 A + cos2 A = 1]
= cos2 A − (1 − sin2 A)
= cos2 A − 1 + cos2 A
= 2 cos2 A − 1
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