Question

If tanx = -4/3 find the value of 9 sec^2x - 4 cotx

Answer 1

Answer:

28

Step-by-step explanation:

tan x = $\frac{-4}{3}$

sec²x = 1 + tan²x

          = 1 + $(\frac{-4}{3} )^{2}$

          = 1 + $\frac{16}{9}$

          = $\frac{9+16}{9}$

          = $\frac{25}{9}$

cot x = $\frac{1}{tanx}$

        = $\frac{1}{\frac{-4}{3} }$

        = $\frac{-3}{4}$

Now,

9 sec²x - 4 cot x

= 9 ×($\frac{25}{9}$) - 4( $\frac{-3}{4}$)

= 25 -(-3)

= 25 + 3

= 28