Find sin x/2, Cos x/2 and tqn x/2 for sin x = -1/4, in quadrant 2nd
Answers
Answered by
0
Answer :
x is in 2nd quadrant then x is between 90 and 180 then cos x is negative and x/2 is between 0 and 90 which means that sin(x/2) , cos (x/2) and tan(x/2) are all positive.
cos x = - sqrt( 1 / (1 + (tan x)^2)) =
= - sqrt( 1/ (1 + 16/9))
= - sqrt( 9 / 25 ) = - 3/5.
(sin x/2)^2 = (1 - cos x)/2 = ( 1 + 3/5)/2
= 4/5
sin x/2 = 2/sqrt(5).
(cos x/2)^2 = (1 + cos x)/2 = ( 1 - 3/5)/2
= 1/5
cos x/2 = 1/sqrt(5).
tan x/2 = (sin x/2)/(cos x/2) = 2.
Answered by
2
ANSWER
Given that x is in second quadrant
90<x<180
45<2x<90
2x lies in first quadrant
So,
sinx,cosx,tanx are positive in first quadrant
tanx=1−tan22x2tan(2x)
3−4=1−tan22x2tan(2x)
Solving the above quadratic equation, we get,
tan(2x)=2−1 or tan(2x)=2
∴tan(2x)=2(∵2x) lies in first quadrant
1+tan2(2x)=sec2(2
Similar questions