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and tan B =-, show that cos 2A = sin 4B.711. If tan A =3third |
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Answer» tanA = 1/7 and tanB = 1/3 show cos2A = sin4B sinA = 1/sqrt50 and cosA = 7/sqrt50 sinB = 1/sqrt10 and cosB = 3/sqrt10 now cos2A = 2cos^2A - 1 = 2{7/sqrt50}^2 -1 = 2* 49/50 = 49/25 -1=24/25 sin4B= 2 sin2B * cos2B = 4 sinB cosB {2 cos^2B - 1} = 4*1/sqrt10 3/sqrt10 [ 2 *9/10 - 1 ] =12/10 [4/5 ] = 24/25 so cos2A = sin4B proved |
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