Question

if tan x = -4/3, find the value of 9 sec^2 x - 4 cot x
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Answer 1

SOLUTION

GIVEN

$tanx \: = - \frac{4}{3}$

TO DETERMINE

$9 {sec}^{2} x - 4cotx$

EVALUATION

$tanx \: = - \frac{4}{3}$

$9 {sec}^{2} x - 4cotx$

$= 9(1 + {tan}^{2} x) - \frac{4}{tanx}$

$= 9(1 + \frac{16}{9} ) - 4 \times ( - \frac{3}{4} \: )$

$= 9 \times \frac{25}{9} + 3$

$= 25 + 3$

$= 28$

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Answer 2

Answer:

The value is $28$.

Step-by-step explanation:

It is given that

$tan x = -4/3$

We need to determine the value of the following expression

$9 sec^2 x - 4 cot x$

We can find all the trigonometric ratio from a single ratio.

We are given $tan x = -4/3$

Now, $9 sec^2 x - 4 cot x$ can be written as

$9 sec^2 x - 4 cot x=9 (1+tan^{2}x ) - 4\frac{1}{tan^{2}x }$

$=9(1+16/9)-4(-3/4)$

$=9*25/9+3$

$=25+3$

$=28$

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