Question

if cos^2theta/(cot^2theta +sin^2theta -1) = 3, 0º < theta < 90°, then the value of (tan theta + cosec theta) is:​

Answer 1

Answer:

Simplifying, we get

cos

2

θ=3cot

2

θ−3cos

2

θ

4cos

2

θ−3cot

2

θ=0

cos

2

θ(4−

sin

2

θ

3

)=0

Hence

cos

2

θ=0

θ=90

0

And

4−

sin

2

θ

3

=0

sin

2

θ=

4

3

sinθ=±

2

3

Hence

θ=±60

0

Now

0<θ<90

0

Hence

θ=60

0

∘

,B=30

∘

Answer 2

The value of $tan(\theta) + csc(\theta) = \sqrt(2/3) + \sqrt(5/2)$

To solve for the value of $(tan \theta + cosec \theta),$we can start by simplifying the given equation:

$cos^2(\theta)/(cot^2(\theta) + sin^2(\theta) - 1) = 3$

We can simplify the cot(theta) term by using the identity $cot(\theta) = 1/tan(\theta).$

$cos^2(\theta)/(1/tan^2(\theta) + sin^2(\theta) - 1) = 3$

We can then multiply both sides of the equation by $(tan^2(\theta) + sin^2(\theta) - 1)$ to get:

$cos^2(\theta) = 3(tan^2(\theta) + sin^2(\theta) - 1)$

We can then use the identity $tan^2(\theta) + 1 = sec^2(\theta)$to get:

$cos^2(\theta) = 3(sec^2(\theta) - 1)$

We can then use the identity $cos^2(\theta) = 1 - sin^2(\theta)$to get:

$1 - sin^2(\theta) = 3(1/cos^2(\theta) - 1)$

We can then solve for $sin(\theta)$ and use the identity $tan(\theta) = sin(\theta) / cos(\theta) and csc(\theta) = 1 / sin(\theta)$  to get the value of $(tan(\theta) + csc(\theta))$

$sin(\theta) = \sqrt(2/5)$

$tan(\theta) = \sqrt(2/5) / \sqrt(1 - 2/5) = \sqrt(2/3)$

$csc(\theta) = 1 / sin(\theta) = \sqrt(5/2)$

so

$tan(\theta) + csc(\theta) = \sqrt(2/3) + \sqrt(5/2)$

This is the final answer.

To know more about tan theta visit : brainly.in/question/48787535

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