If cos theta<0 and cot theta=12/5 . then{sin theta+cos(-theta)}/{5 sec(-theta)+tan theta} = ?
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cot theta=12÷5,
tan theta =5÷12,
sec theta = -(13÷12),
cos theta= -(12÷13),
sin theta = -(5÷13),
cos(-theta)=cos theta.
sec(-theta)=sec theta.
[sin theta +cos theta ]/[5sec theta +tan theta]=[-(5÷13)-(12÷13)]/[-(65÷12)+(5÷12)]=[-(17÷13)]/[-5]=17÷65
tan theta =5÷12,
sec theta = -(13÷12),
cos theta= -(12÷13),
sin theta = -(5÷13),
cos(-theta)=cos theta.
sec(-theta)=sec theta.
[sin theta +cos theta ]/[5sec theta +tan theta]=[-(5÷13)-(12÷13)]/[-(65÷12)+(5÷12)]=[-(17÷13)]/[-5]=17÷65
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