Question

if 4tan theta =3, evaluate(4sin....​

Answer 1

Answer:

13/11

Step-by-step explanation:

tan@ = 3/4

tan^2@ = 9/16

sec^2@ - 1 = 9/16

sec@ = 5/4

Now put it in question

(4tan@ -1 + sec@)/(4tan@ + 1 - sec@)

(3 - 1 + 5/4 )/(3+ 1 - 5/4)

(13/4)/(11/4)

13/11

Answer 2

Answer:

13/11

Step-by-step explanation:

4tan∅ = 3 ---( 1 )

tan∅ = 3/4

Square both sides.

=> tan² ∅ = 9/16

=> sec²∅ - 1 = 9/16

=> sec²∅ = 9/16 + 1

=> sec²∅ = ( 9 + 16)/16

=> Sec²∅ = 25/16

=> Sec∅ = 5/4 ---( 2 )

Now ,

=> (4sin∅-cos∅+1)/(4sin∅+cos∅-1)

Divide numerator and denominator With cos∅, we get

(4tan∅-1+sec∅)/(4tan∅+1-sec∅)

=> (3-1+5/4)/(3+1-5/4)

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

Divide numerator and denominator With 4 , we get

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

=> 13/11

Hence, the answer is 13/11.

#Hope my answer helped you!