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If `tan theta=1`, then `(sin theta+cos theta)/(sec theta+cosec theta)=` |
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Answer» `tan theta=1` From the table of trigonometric ratios, We know that `tan 45^(@)=1` `:.theta=45^(@)` `sin theta=sin 45^(@)=1/(sqrt(2))` `cos theta=cos45^(@)=1/(sqrt(2))` `sec theta =sec 45^(@)=sqrt(2)` `cosec theta=cosec 45^(@)=sqrt(2)` `(sin theta+cos theta)/(sec theta+cosec theta)=(sin 45^(@)+cos 45^(@))/(sec 45^(@)+cosec 45^(@))` `=(1/(sqrt(2))+1/(sqrt(2)))/(sqrt(2)+sqrt(2))` `=((2/(sqrt(2))))/(sqrt(2))` `=2/(sqrt(2))-:2sqrt(2)` `=2/(sqrt(2))xx1/(2sqrt(2))` `=1/2` `(sin theta+cos theta)/(sec theta+cosec theta)=1/2` |
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