If 5k = tanθ and (5/k)= secθ, then what is the value of 10 (k2 – 1/k2)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. -(2/5)
Given that
If 5k = tanθ........(1
(5/k)= secθ.........(2
After Subtracting the square of the equation (2 & (1
tan2θ - sec2θ = 25 (k2 – 1/k2)
As we know,
sec2θ - tan2θ = 1
-1 = 25 (k2 – 1/k2)
k2 – 1/k2 = -1/25
10 (k2 – 1/k2) = -10/25 = - (2/5)