Question

If secθ = 13/5, find the value of 2sinθ+3cosθ/5cosθ-4 sinθ

Answer 1

secθ = 13/5
we know, secθ = hypotenuse/base
so, secθ = 13/5 = hypotenuse/base
e.g., hypotenuse = 13
and base = 5

we know, according to Pythagoras theorem,
perpendicular = √{hypotenuse²-base²}
= √{13² - 5²} = 12

hence, sinθ = perpendicular /hypotenuse
so, sinθ = 12/13 and cosθ = 1/secθ = 5/13

now, (2sinθ + 3cosθ)/(5cosθ - 4sinθ)

= (2 × 12/13 + 3 × 5/13)/(5 × 5/13 - 4 × 12/13)

= (24 + 15)/(25 - 48)

= 39/-23

= -39/23

Answer 2

Answer:

Step-by-step explanation:

if secθ -tanθ =4, then find the value of cos θ