Question

sec 220⁰/
cos 580°-
tan 940°/
cot 220°​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{\dfrac{sec\,220^\circ}{cos\,580^\circ}-\dfrac{tan\,940^\circ}{cot\,220^\circ}}$

$\underline{\textbf{To find:}}$

$\textsf{The value of}$

$\mathsf{\dfrac{sec\,220^\circ}{cos\,580^\circ}-\dfrac{tan\,940^\circ}{cot\,220^\circ}}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Formula used:}}$

$\boxed{\mathsf{sec^2\theta-tan^2\theta=1}}$

$\mathsf{Consider,}$

$\mathsf{\dfrac{sec\,220^\circ}{cos\,580^\circ}-\dfrac{tan\,940^\circ}{cot\,220^\circ}}$

$\mathsf{=\dfrac{sec\,220^\circ}{cos(1{\times}360^\circ+220^\circ)}-\dfrac{tan(2{\times}360^\circ+220^\circ)}{cot\,220^\circ}}$

$\mathsf{=\dfrac{sec\,220^\circ}{cos\,220^\circ}-\dfrac{tan\,220^\circ}{cot\,220^\circ}}$

$\mathsf{=\dfrac{sec\,220^\circ}{\dfrac{1}{sec\,220^\circ}}-\dfrac{tan\,220^\circ}{\dfrac{1}{tan\,220^\circ}}}$

$\mathsf{=sec^2220^\circ-tan^2220^\circ}$

$\textsf{=1}\;\;(\textsf{Using the formula})$

$\boxed{\mathsf{\dfrac{sec\,220^\circ}{cos\,580^\circ}-\dfrac{tan\,940^\circ}{cot\,220^\circ}=1}}$

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Answer 2

Answer:

Step-by-step explanation:

LHS=sec(180+40)/cos(360+220) - tan(720+220)/cot(180+40)

= sec40/cos220 - tan220/cot40

=. -- sec40/-cos40 - tan 40/cot40

sec^2 40-tan^2 40 = 1 =RHS