CBSE Class 11-science Answered
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1. sin A/ cos A = 8/15
⇒tan A = 8/15
We know that, sec2A = 1+ tan2A
= 1 + (8/15)2
= 1 + 64/ 225
= 289/225
Therefore, sec A = 17/15
Hence, cos A = 15/17
sin2A = 1- cos2A
= 1 - 225/ 289
= 64/ 289
Therefore, sin A = 8 / 17
2. if sec A+ tanA= m
To prove: sinA = m2-1/ m2+1
sec A+ tanA = m
= 1/cos A + sinA/ cos A = m
= (1+ sinA)/ cos A = m
= (1+ sinA)/ 1 - sin2A = m
= (1+ sinA) (1+sinA)/ (1-sinA) (1+ sinA) = m
= (1+sinA)/ (1-sinA) = m
⇒ (1+ sin A) / 1-sinA = m2
Now from componendo and dividendo we know that
if a+b/ a- b = c/d then, a/b = c+d/c-d
Therefore,
1/ sinA = m2 + 1/ m2 -1
⇒sinA = m2 - 1/ m2 +1
Similarly do the last one.