3-4 sin^2theeta/cos^2theeta=3-tan^2theeta proove that
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Step-by-step explanation:
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Answer:
proved
Step-by-step explanation:
3 - 4 sin^2 (A)
= 3 - 4 (1 - cos^2 (A))
= 3 - 4 + 4 cos^2 (A)
= 4 cos^2 (A) - 1
= 3 cos^2 (A) + cos^2 (A) - 1
= 3 cos^2 (A) - (1 - cos^2 (A))
= 3 cos^2 (A) - sin^2 (A)
= cos^2 (A) [3 - tan^2 (A)] [Since, sin^2 (A) / cos^2 (A) = tan^2 (A)]
Hence, 3 - 4 sin^2 (A) = cos^2 (A) [3 - tan^2 (A)]
Divide both sides by cos^2 (A).
(3 - 4 sin^2 (A)) ÷ (cos^2 (A)) = 3 - tan^2A [Proved]
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