If Tan(x) = 2, and 0 < x < 2pi, find the exact value of Sin(x + pi/4)?

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Answer 1 · 2018-06-17T08:33:04

Let #z=x+pi/4#

So #tanz=tan(x+pi/4)#

#=>tanz=(tanx+tan(pi/4))/(1-tanxtan(pi/4))#

#=>tanz=(tanx+1)/(1-tanx)#

#=>tanz=(2+1)/(1-2)=-3#

So #zin "quadrant II or IV"#

Now #cotz==1/tanz=-1/3#

So #cscz=pmsqrt(1+cot^2z)#

#=>cscz=pmsqrt(1+(-1/3)^2)#

#=>cscz=pmsqrt10/3#

#=>sinz=pm3/sqrt10#

#=>sin(x+pi/4)=pm3/sqrt10#

#z or (x+pi/4)in "quadrant II or IV"#