Question

if tan A = 3÷4' find the value of 1÷ sin A + 1÷ cosA​

Answer 1

Solution:

Given: tan(A) = 3/4

1/sin(A) + 1/cos(A) = ?

tan(θ) is positivie in Quadrant 1 and Quadrant 3

tan(θ) = 3/4

Quadrant 1

sec^2(θ) = 1 + tan^2(θ)

= 1 + (3/4)^2

= 1 + (9/16)

= (16+9)/16

= 25/16

sec(θ) = (√25/16) = 5/4

cos(θ) = 1/sec(θ) = 1/(5/4) = 4/5

sin(θ) = tan(θ) * cos(θ) = (3/4) * (4/5)

= 12/20 = 3/5

Now substitute all these expression values in

1/sin(A) + 1/cos(A)

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

= 5/3 + 5/4

= 35/12

Therefore,

1/sin(A) + 1/cos(A) = 35/12

Hope this will help.