Question
Mon August 31, 2009 By: Navjot

please solve these questions

Expert Reply
Tue September 01, 2009

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, 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/ m-1

⇒sinA = m- 1/ m+1

Similarly do the last one.

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