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        If cot^2 theta = cot(theta-alpha) cot(theta-beta) show that cot 2theta = 1/2(cot alpha+ cot beta)
one year ago

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.

one year ago
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### Course Features

• 31 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions