Question

if 4 tan theta =3 ,evaluate (4sin theta-cos theta + 1/4sin theta )​

Answer 1

Answer:[ Here I am using A instead of

theta ]

It is given that ,

4tanA = 3 ---( 1 )

tanA = 3/4

=> tan² A = 9/16

=> sec²A - 1 = 9/16

=> sec²A = 9/16 + 1

=> sec²A = ( 9 + 16)/16

=> Sec²A = 25/16

=> SecA = 5/4 ---( 2 )

Now ,

(4sinA-cosA+1)/(4sinA+cosA-1)

Divide numerator and denominator

With cosA, we get

(4tanA-1+secA)/(4tanA+1-secA)

= (3-1+5/4)/(3+1-5/4) [from(1)&(2)]

= (2+5/4)/(4-5/4)

Divide numerator and denominator

With 4 , we get

= ( 8 + 5 )/( 16 - 5 )

= 13/11