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 please solve these questions
 Entrance Exam
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please solve these questions
We cannot entertain more than 5 questions in a subject per day. In case of multiple questions within a query, please post each question individually and let us know where you are getting stuck so that we would be able to explain things better.
1. sin A/ cos A = 8/15
⇒tan A = 8/15
We know that, sec^{2}A = 1+ tan^{2}A
= 1 + (8/15)^{2}
^{ }= 1 + 64/ 225
= 289/225
Therefore, sec A = 17/15
Hence, cos A = 15/17
sin^{2}A = 1 cos^{2}A
= 1  225/ 289
= 64/ 289
Therefore, sin A = 8 / 17
2. if sec A+ tanA= m
To prove: sinA = m^{2}1/ m^{2}+1
sec A+ tanA = m
= 1/cos A + sinA/ cos A = m
= (1+ sinA)/ cos A = m
= (1+ sinA)/ 1  sin^{2}A = m
= (1+ sinA) (1+sinA)/ (1sinA) (1+ sinA) = m
= (1+sinA)/ (1sinA) = m
⇒ (1+ sin A) / 1sinA = m^{2}
Now from componendo and dividendo we know that
if a+b/ a b = c/d then, a/b = c+d/cd
Therefore,
1/ sinA = m^{2 }+ 1/ m^{2 }1
⇒sinA = m^{2 } 1/ m^{2 }+1
Similarly do the last one.