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manoj jangra Grade: 12
```        1.Prove that for real x, tan(x+a)/tan(x-a) when x≠∏/4, 3∏/4 cannot lie between (1-sin2a)/(1+sin2a) and (1+sin2a)/(1-sin2a)
2.Find the set of possible values of tan(x+∏/6)/tanx  where x is any real angle.```
7 years ago

## Answers : (1)

147 Points
```										Dear manoj
let
y = tan(x+a) /tan(x-a)
=  sin(x+a)cos(x-a) / cos(x+a) sin(x-a)
=[sin2x +  sin2a]/[sin2x -sin2a]
use componendo and divedendo
(y+1)/(y-1)  = sin2x /sin2a
or
sin2x = (y+1)sin2a /(y-1)
for  every real value of x
-1≤  sin2x ≤1
so  -1≤  (y+1)sin2a  /(y-1) ≤1
simplyfy each side of inequality
(1-sin2a)/(1+sin2a)  ≤  y  ≤   (1-sin2a)/(1+sin2a)
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7 years ago
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