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```
If A+B+C=pi Show that tanA=tanB+tanC If (cot(alpha-beta)/ cot alpha ) +(cos^2gama/cos^2 alpha)=1

```
9 months ago

## Answers : (2)

Arun
25768 Points
```							3 tanФ = Cot Ф = 1/tanФ3 tan²Ф = 1TanФ = + 1/√3 Ф = n π + π/6Ф = π/6 or π+π/6 = 7π/6 or π-π/6 = 5π/6 or 2π-π/6 = 11π/6 There are 4 solutions for 0° =============== A + B + C = π/2  => Tan(A+B) = Tan(π/2-C) = Cot C = 1/TanC  => Tan (B+C) = 1/TanA  => Tan(C+A) = 1/TanB Tan (A+B) = [TanA + TanB]/[1 - TanA TanB]Rearrange:  TanA TanB = 1 - (TanA+TanB)/Tan(A+B)                                      = 1 - (TanA+TAnB) ×TanC     ---(1) Similarly:   Tan B TanC = 1 - (TanB + TanC) × TanA  ---(2)                  Tan C TanA = 1 - (TanC + TanA) ×TanB  --- (3) Add (1) , (2) & (3):LHS = TanA TanB + TanB TanC + TanC Tan A        = 3 - 2 (TanA TanB + TanB TanC + Tanc TanA)        = 3 -  2 LHS So  TanA TanB + TanB TanC + Tan C TanA = 1
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9 months ago
Vikas TU
14146 Points
```							Dear student https://www.askiitians.com/forums/Trigonometry/sina-2sin3a-sin5a-sin3a-2sin5a-sin7a-sin3a_179603.htmGood Luck
```
8 months ago
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• 31 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions