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Find the value `tan(22(1)/(2))`.A. `sqrt2-1`B. `1+sqrt2`C. `2+sqrt3`D. `2-sqrt3` |
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Answer» Correct Answer - A We have, `tan2theta=(2tantheta)/(1-tan^(@)theta)` Let `theta=(22(1)/(2))rArr2theta=45^(@)` `thereforetan45^(@)=(2tantheta)/(1-tan^(2)theta)`. `1=(2tantheta)/(1-tan^(2)theta)` `rArr1-tan^(2)theta=2tantheta` `rArrtan^(2)theta+2tantheta-1=0` `tantheta=(-2pmsqrt(2^(2)-4(1)(-1)))/(2(1))` `=(-2pmsqrt8)/(2)=-1pmsqrt2`. As `theta " is " (22(1)/(2)), tan(22(1)/(2))^(@)=sqrt2-1`. |
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