Question

If cot= 3/4 and π< 0 < 3π/4then find the
value of 4coseco +5coso.​

Answer 1

cot A = 3 / 4

NOTE : here instead of theta I have supposed theta as " A " .

" A " lies in 3rd quadrant.

cosec^2 A - cot^2 A = 1

:. cosec^2 A = 1 + ( 3/4 )^2

= 1 + ( 9/16 )

= 16+9 / 16

cosec^2 A = 25 / 16

taking sq. rt.

:. cosec A = - 5 / 4

---------. in 3rd quad.

cosec is -ve

:. sin A = 1 / cosec A = 1 / ( -5/4 )

= - 4 / 5

Now,

sin^2 A + cos^2 A = 1

:. cos^2 A = 1 - (- 4/5 )^2

= 1 - ( 16/25 )

= 25-16 / 25

:. cos^2 A = 9 / 25

taking sq. rt.

:. cos A = - 3 / 5

-------- in 3rd quad.

cos is -ve

4 cosec A + 5 cos A = 4 ( - 5/4 ) + 5 ( - 3/5 )

= - 5 + ( - 3 )

= - 5 - 3

= - 8