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If x lie in interval 0 to pi and cosx+sinx=0.5 then find the value of tanx

If x lie in interval 0 to pi and cosx+sinx=0.5 then find the value of tanx

Grade:12

1 Answers

Ajay Verma
askIITians Faculty 33 Points
10 years ago
soln:

cosx+sinx= 1/2
square both sides..

(cosx+sinx)^2 = 1/4
1+ 2*sinx*cosx = 1/4
sin 2x = -3/4
2 tan x/(1+tan2x) = -3/4
-8 tan x = 3(1+tan2x)
3 tan2x + 8 tan x + 3 = 0

solving this
tan x = {-8 + 2(7)1/2}/ 6 & {-8 - 2(7)1/2}/ 6



Thanks and Regards,
Ajay verma,
askIITians faculty,
IIT HYDERABAD

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