Question

5cos theta + 12sin theta = 13 find cosec theta =?

Answer 1

Step-by-step explanation:

I am usin x in cas of theta-------------->

so 5 cosx=13-12 sinx

squaring on both sides we get,

25 cos²x=169+144 sin²x-312 sinx

in case of cos²x we substitute (1-sin²x),as sin²x+cos²x=1

equation will be 169 sin²x-312 sinx+144=0

after using quadratic formula we get sinx=312/338

so sinx =12/13.

done!!!!!!!!!!!! 

Hope this answer helps you!!!

Answer 2

The value of cosec = 13/12

Given:

5 cos θ+ 12 sin θ = 13

To find:

Find the value of cosec

Solution:

Given 5 cos θ+ 12 sin θ = 13  

⇒ 5 cos θ = 13 - 12 sin θ  

Do squaring on both sides

⇒  (5 cos θ)² = (13 - 12 sin θ)²

⇒ 25 cos²θ = 169 + 144 sin²θ - 2(13)(12 sin θ)  

⇒ 25 cos²θ = 169 + 144 sin²θ - 312 sin θ  

As we know cos²θ = 1 - sin²θ  

⇒ 25 (1-sin²θ) = 169 + 144 sin²θ - 312 sin θ  

⇒ 25 - 25 sin²θ = 169 + 144 sin²θ - 312 sin θ

⇒ 25 = 169 + 169 sin²θ - 312 sin θ

⇒ 169 sin²θ - 312 sin θ + 144 = 0

⇒ (13 sin θ)² - 2 (13 sin θ) + 12² = 0

Which is in the form of (a-b)² = a²+b²-2ab

⇒ (13 sin θ - 12)² = 0

⇒ 13 sin θ - 12 = 0

⇒ sin θ = 12/13

As we know cosec θ = 1/sin θ

cosec = 1/(12/13) = 13/12

Therefore,

The value of cosec = 13/12

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