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`        If xy>1 then prove that tan^-1x+tan^-1y=tan^-1 (x+y)÷(1-xy)`
6 months ago

Umar
12 Points
```							There is an error in this question. By mistake I had left π in the right hand side. I had also posted the right question
```
6 months ago
Arun
23013 Points
```							(i) tan-1x + tan-1y = tan-1((x+y)/(1-xy)), xy .Let tan-1x = A and tan-1y = BÞ tan A = x and tan B = yNow, tan(A+B) = (tanA + tanB)/(1-tanAtanB)⇒ tan(A+B) = (x+y)/(1-xy)⇒tan-1[(x+y)/(1-xy)] = A + B⇒tan-1[(x+y)/(1-xy)] = tan-1x + tan-1y (ii) tan-1x - tan-1y = tan-1((x-y)/(1+xy)), xy > -1.Proof:Let tan-1x = α ⇒ x = tan α     tan-1y = β ⇒ y = tan βNow, tan(α - β) = (tan α - tan β)/(1+ tanαtanβ) = (x-y)/(1+xy)α - β = tan-1 [(x-y)/(1+xy)]tan-1x - tan-1y = tan-1 [(x-y)/(1+xy)]Hence, tan-1x - tan-1y = tan-1 [(x-y)/(1+xy)], xy > -1
```
6 months 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