Question

If tan^2 θ − 3 tan θ + 1 = 0, find the value of tan θ + cot θ

Answer 1

Answer:

Step-by-step explanation:
I'm using @ for theta.

Let's rewrite write the equation in terms of sin@ and cos@.

$tan^{2}@ -3tan@ + 1 =0$

$\frac{sin^{2}@}{cos^{2}@} -3\frac{sin}{cos} +1 = 0$

$\frac{sin^{2}@}{cos^{2}@} -3\frac{sin}{cos} = -1$

Taking sin/cos from both terms, we get

$\frac{sin}{cos} (\frac{sin@}{cos@} -3)= -1$

Multiplying both sides by cos/sin

$1(\frac{sin@}{cos@} -3)= -\frac{cos}{sin}$

$\frac{sin@}{cos@} +\frac{cos}{sin} = 3$

We can write the above equation as:
$tan @ + cot@ = 3$

Hence, tan + cot = 3

This is my first answer, hope it helps ☺️.

Answer 2

The value of tan θ + cot θ = 3

Given:

tan² θ − 3 tan θ + 1 = 0

To find:

Find the value of tan θ + cot θ  

Solution:

The expression is tan² θ − 3 tan θ + 1 = 0  

=> [sin θ/cos θ]² − 3[ sin θ/cosθ ] = - 1    [ ∵ tan θ = sin θ/cos θ ]  

=> sin θ/cos θ [ sin θ/cos θ] − 3 = - 1   [ take sin θ/cos θ common ]

=> [ sin θ/cos θ] − 3 = - 1 [ cos θ/sin θ ]  

=> [ sin θ/cos θ] − 3 = - cos θ/sin θ

=> [ sin θ/cos θ] + [ cos θ/sin θ ] = 3  

=> tan θ + cot θ = 3   [ ∵ cos θ/sin θ = cot θ ]

Therefore,

The value of tan θ + cot θ = 3  

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https://brainly.in/question/5410984  

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