Question

Need help:

Find the exact value of sec(2tan^-1 (3/4)

Answer 1

hmmm lemme take a poke

Answer 2

$$\bf
sec\left(2tan^{-1}\left(\cfrac{3}{4}\right)\right)\\
sec(2\theta) \implies \cfrac{1}{cos(2\theta)}\\
cos(2\theta) = 1- 2 sin^2(\theta)\\
\text{now let's check above}\\
\color{green}{
tan^{-1}\left(\cfrac{3}{4}\right) \implies \cfrac{b}{a}\\
c = \sqrt{4^2+3^2} = 5
}
$$

Answer 3

so \(\bf cos(2\theta) = 1- 2 sin^2(\theta)
\implies cos(2\theta) = 1- 2\left(\cfrac{3}{5}\right)^2\)

Answer 4

so, that'd give you the cosine, flip it around to the secant

Answer 5

gives me 7/25, so the secant will be 25/7