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If 0 leq theta leq pi and sin(theta/2)...

If `0 leq theta leq pi and sin(theta/2)=sqrt(1+sintheta)-sqrt(1-sintheta)` ,then the possible value of `tan theta` , is -

A

a. `(4)/(3)`

B

b. 0

C

c. `(-3)/(4)`

D

d.`(-4)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
B, D
`sin.(theta)/(2)=sqrt(1+sin theta)-sqrt(1-sin theta)`
`rArr sin.(theta)/(2)=|cos.(theta)/(2)+sin.(theta)/(2)|-|cos.(theta)/(2)-sin.(theta)/(2)|`
If `0 le theta le (pi)/(2), sin.(theta)/(2)=2 sin.(theta)/(2) rArr theta = 0`
If `(pi)/(2) lt theta le pi, sin.(theta)/(2) = 2 cos.(theta)/(2)`
`rArr tan.(theta)/(2)=2`
`rArr tan theta = (2 tan.(theta)/(2))/(1-"tan"^(2)(theta)/(2))=(4)/(1-4)=(-4)/(3)`
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