Question

it tan x = 3/4 , π<x<3π/2 . find the value sin x/2, cos π/2, tan π/2.

Answer 1

Given π<x<3π2andtanx=34

π<x<3π2

⇒π2<x2<3π4→x2∈ 2nd quadrant

This means

sin(x2)→+ve

cos(x2)→−ve

tan(x2)→−ve

Now tanx=34

⇒2tan(x2)1−tan2(x2)=34

⇒8tan(x2)=3−3tan2(x2)

⇒3tan2(x2)+8tan(x2)−3=0

⇒3tan2(x2)+9tan(x2)−tan(x2)−3=0

⇒3tan(x2)(tan(x2)+3)−1(tan(x2)+3)=0

⇒(3tan(x2)−1)(tan(x2)+3)=0

This means

tan(x2)=13→not acceptable as tan(x2)→−ve

So tan(x2)→−3

Now

cos(x2)=1sec(x2)=−1√1+tan2(x2)

=−1√1+(−3)2=−1√10

Again

sin(x2)=tan(x2)×cos(x2)

=−3×(−1√10)=3√10

I hope this is correct and if it helped you please mark it brainliest