ICSE Class 10 Answered
tan a + sin a = m & tan a - sin a = n prove that m2 - n2 4
Asked by Vinay | 06 Apr, 2017, 01:47: PM
Expert Answer
Given that tan a + sin a = m and tan a - sin a = n
Consider,
mn = (tan a + sin a) (tan a - sin a)
mn = tan2 a - sin2 a =
mn =
mn =
mn = tan2 a × sin2 a .......( i )
Consider,
LHS = m2 - n2
= (tan a + sin a )2 - (tan a - sin a)2
= tan2 a + sin2 a + 2 tan A sin A - tan2 a - sin2 a + 2 tan A sin A
= 4 tan A sin A
= 4 [from equation ( i )]
= RHS
Hence proved.
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Answered by | 06 Apr, 2017, 02:11: PM
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