Question

If 5 sec θ – 3 tan θ = 5, then what is the value of 5 tan θ – 3 sec θ?

Answer 1

5 sec θ -3 tan θ =5 ….1

5 tan θ -3 sec θ = x …2

On squaring both equations and subtracting 2 from 1,

(5 sec θ – 3 tan θ)^ 2- (5 tan θ – 3 sec θ)^ 2=25 – X^2

(25 sec 2 θ – 2*5 sec θ*3 tan θ + 9 tan 2 θ) – (25 tan 2 θ – 2*5 sec θ*tan θ+ 9 sec 2 θ)=25-X^2

X^ 2 =25-16=9

X =√9 =±3