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Grade: 11
        
If cot^2 theta = cot(theta-alpha) cot(theta-beta) show that cot 2theta = 1/2(cot alpha+ cot beta)
27 days ago

Answers : (1)

Bhagyashri verma
24 Points
							
Hi,
Using the given equation, and using the formulas, we get,
 
 cot^2\Theta = cot(\Theta -\alpha ) cot(\Theta -\beta )
cot^2\Theta = (cot\Theta cot\alpha +1 / cot\Theta -cot\alpha )* ((cot\Theta cot\beta +1 )/ cot\Theta -cot\beta)= (cot^2\Theta cot\alpha cot\beta+ cot\Theta cot\beta+ cot\Theta cot\alpha+1)/(cot\alpha cot\beta +cot^2\theta-cot\Theta cot\beta- cot\Theta cot\alpha)
on rearranging,
 
 cot^4\theta -1 = cot\alpha cot\theta ( 1+ cot^2 \theta)+cot\theta cot\alpha (1+cot^2\theta)
cot^2\theta -1 = cot\theta (cot\alpha+ cot\beta)
(cot^2\theta -1)/cot\theta = (cot\alpha+ cot\beta)
cot2\theta = 1/2(cot\alpha+ cot\beta)
In case to any difficulty, feel free to ask.
 
27 days ago
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