Question

if tan 70°-tan20°=K,tan50°Then k=?
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Answer 1

$\textbf{Given:}$

$\mathsf{tan70^\circ-tan20^\circ=k\;tan50^\circ}$

$\textbf{To find:}$

$\textsf{The value of k}$

$\textbf{Solution:}$

$\textbf{Formula used:}$

$\boxed{\begin{minipage}{7cm} \\\mathsf{If\;A+B=90^\circ,\,then\;tanA\;tanB=1}\\ \end{minipage}}$

$\mathsf{Consider,}$

$\mathsf{tan70^\circ-tan20^\circ=k\;tan50^\circ}$

$\mathsf{tan70^\circ-tan20^\circ=k\;tan(70^\circ-20^\circ)}$

$\mathsf{tan70^\circ-tan20^\circ=k\left(\dfrac{tan70^\circ-tan20^\circ}{1+tan70^\circ\,tan20^\circ}\right)}$

$\textsf{Using the above formula,}$

$\mathsf{tan70^\circ-tan20^\circ=k\left(\dfrac{tan70^\circ-tan20^\circ}{1+1}\right)}$

$\mathsf{tan70^\circ-tan20^\circ=k\left(\dfrac{tan70^\circ-tan20^\circ}{2}\right)}$

$\mathsf{2(tan70^\circ-tan20^\circ)=k(tan70^\circ-tan20^\circ)}$

$\implies\boxed{\mathsf{k=2}}$

$\textbf{Find more:}$

If tanA = cotB , Prove thet A + B = 90°

https://brainly.in/question/8544040

यदि A+B+C= 90 तो सिद्ध कीजिए: tanAtanB+tanBtanC+tanCtanA=1

https://brainly.in/question/15268179