If (cosec A + cot A) (cosec B + cot B) (cosec C + cot C) = (cosec A – cot A) (cosec B – cot B) (cosec C – cot C), then the value of each side of the above equation can be
Question
If (cosec A + cot A) (cosec B + cot B) (cosec C + cot C) = (cosec A – cot A) (cosec B – cot B) (cosec C – cot C), then the value of each side of the above equation can be
Solution
The given equation is (cosec A + cot A) (cosec B + cot B) (cosec C + cot C) = (cosec A – cot A) (cosec B – cot B) (cosec C – cot C).
We know that cosec^2 θ - cot^2 θ = 1 for all values of θ where cosec θ and cot θ are defined.
So, we can write the given equation as:
(cosec A + cot A) (cosec B + cot B) (cosec C + cot C) = (cosec A – cot A) (cosec B – cot B) (cosec C – cot C)
=> (cosec^2 A - cot^2 A) (cosec^2 B - cot^2 B) (cosec^2 C - cot^2 C) = 1
=> 1 * 1 * 1 = 1
So, the value of each side of the above equation is 1.
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