Question

Tan25+tan35-√3=k×tan25×tan35 then k equals to what

Answer 1

$\textbf{Given:}$

$\tan\,25+\tan\,35-\sqrt{3}=k{\times}\tan\,25{\times}\tan\,35$

$\textbf{To find:}$

$\text{The value of k}$

$\textbf{Solution:}$

$\text{Consider,}$

$\tan\,25+\tan\,35-\sqrt{3}=k{\times}\tan\,25{\times}\tan\,35$

$\text{Using the identity,}$

$\boxed{tan(A+B)=\dfrac{tanA+tanB}{1-tanA\,tanB}\implies\;tanA+tanB=tan(A+B)(1-tanA\,tanB)}$

$\tan(25+35)(1-\tan\,25\,\tan\,35)-\sqrt{3}=k{\times}\tan\,25{\times}\tan\,35$

$\sqrt{3}(1-\tan\,25\,\tan\,35)-\sqrt{3}=k{\times}\tan\,25{\times}\tan\,35$

$\sqrt{3}-\sqrt{3}\tan\,25\,\tan\,35-\sqrt{3}=k{\times}\tan\,25{\times}\tan\,35$

$-\sqrt{3}\tan\,25\,\tan\,35=k{\times}\tan\,25{\times}\tan\,35$

$\implies\bf\,k=-\sqrt{3}$

$\textbf{Answer:}$

$\textbf{The value of k is \bf-\sqrt{3} }$

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Answer 2

Step-by-step explanation:

k = -√3

hope this helps you