Question

If tan theta =4\3find the value of sin theta+cos theta \ sin theta -cos theta

Answer 1

tan A = 4 / 3

NOTE : Here , instead of theta I have supposed theta as A.

:. sec^2 A - tan^2 A = 1

:. sec^2 A = 1 + tan^2 A

= 1 + ( 4/3 )^2

= 1 + ( 16/9 )

= 9+16 / 9

sec^2 A = 25 / 9

taking sq. rt.

:. sec A = 5 / 3

:. cos A = 1 / sec A = 1 / ( 5/3 )

= 3 / 5

NOW ,

sin^2 A + cos^2 A = 1

:. sin^2 A = 1 - cos^2 A

= 1 - ( 3/5 )^2

= 1 - ( 9/25 )

= ( 25-9) / 25

:. sin^2 A = 16 / 25

taking sq. rt.

:. sin A = 4 / 5

sin A + cos A / sin A - cos A

= [ 4 / 5 + 3 / 5 ] / [ 4 / 5 - 3 / 5 ]

= ( 7/5 ) / ( 1/5 )

= 7 / 1

= 7