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