Question

Given : 17 cos θ = 15;
Find the value of: tan θ + 2 secθ .

Answer 1

Consider the diagram below :

17 cos θ = 15

cos θ = `(15)/(17)`

i.e `"base"/"hypotenuse" = (15)/(17) ⇒ "AB"/"AC" = (15)/(17)`

Therefore if length of AB = 15x, length of AC = 17x

Since
AB² + BC² = AC²  ...[ Using Pythagoras Theorem ]

(17x)² – (15x)² = BC²

BC² = 64x²

∴ BC = 8x     ...( perpendicular)

Now

sec θ  = `"AC"/"AB" = (17)/(15)`

tan θ  = `"BC"/"AB" = (8)/(15)`

Therefore
tan θ +2 sec θ 

= `(8)/(15) + 2. (17)/(15)`

= `(42)/(15)`

= `(14)/(5)`

= `2(4)/(5)`