Question

If sin theta +cos /sin-cos =5/3 find the value of 7tan+2/2tan+7

Answer 1

sin theta+cos theta /sin theta-cos theta =5/3
=>3 (sin theta+cos theta)=5(sin theta-cos theta)
=> 8 cos theta= 2 sin theta
=>sin theta/cos theta =8/2=4= tan theta
=> 7 tan theta+2/2 tan theta +7= 7(4)+2/2(4)+7
=> 7 tan theta+2/2 tan theta +7= 30/15=2

Answer 2

sin a + cos a/sin a - cos a = 5/3

cross multiply

3(sin a + cos a) = 5(sin a - cos a )

=> 3 sin a + 3 cos a = 5 sin a - 5 cos a

=> 5 cos a + 3 cos a = 5 sin a - 3 sin a

=> 8 cos a = 2 sin a

=> 8 cos a/2 = sin a

=> sin a = 4 cos a

=> sin a/cos a = 4

tan a = 4

now substituting value of tan a

7(tan a) + 2/2(tan a) + 7

=7(4) + 2/2(4)+7

=30/15

=2