Question

of sin theta is equal to minus 3/5 and theta lies in 4th quadrant, then cos theta + cot theta equals ​

Answer 1

Step-by-step explanation:

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Answer 2

Given :

sin θ = $\frac{-3}{5}$  ; and

θ lies in 4th quadrant .

To find :

Value of cos θ + cot θ

Explanation :

Step 1

We know , sin²θ + cos²θ = 1

therefore , cos²θ = 1 - sin²θ

     hence , cos²θ = 1 -  $(\frac{-3}{5}) ^{2}$

 therefore , cosθ = ± $\frac{4}{5}$

Here , cosθ shall have positive values only since θ lies in 4th quadrant and we know that in 4th quadrant , any value of cos is positive .

Hence cosθ = $\frac{4}{5}$

Step 2

cotθ = cosθ/sinθ

Hence , cotθ = $\frac{-4}{3}$

Step 3

cosθ + cotθ = $\frac{4}{5} + ( \frac{-4}{3} )$

                   = $\frac{-8}{15}$

Final answer :

Hence, the value of cosθ + cot θ = $\frac{-8}{15}$