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Find the value of tan `75^(@)`. |
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Answer» We have, `tan75^(@)=tan(45^(@)+30^(@))` `(tan45^(@)+tan30^(@))/(1- tan45^(@)*tan30^(@))` `=(1+(1)/(sqrt(3)))/(1-1xx(1)/(sqrt(3)))=(sqrt(3)+1)/(sqrt(3)-1)` `((sqrt(3)+1)/(sqrt(3)-1))((sqrt(3)+1)/(sqrt(3)+1))=(3+1+2sqrt(3))/(2)=2+sqrt(3)` `:. tan 75^(@)=(sqrt(3+1))/(sqrt(3-1)) or 2+sqrt(3)`. |
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