Somebody plz try out proving this indentity....

**snigdha** · February 9th 2010, 07:28 AM

If tanΘ = 4/3,

then prove that:√(1-sin Θ)/(1+sin Θ) = 1/3

**Plato** · February 9th 2010, 07:52 AM

There is difficulity with this problem as stated.
If $\tan(\theta)=\frac{4}{3}$ then $\sin(\theta)=\pm\frac{4}{5}$ .
That identity is true for only one of those values.
Did you leave some information out?

**snigdha** · February 9th 2010, 08:00 AM

Originally Posted by Plato

There is difficulity with this problem as stated.
If $\tan(\theta)=\frac{4}{3}$ then $\sin(\theta)=\pm\frac{4}{5}$ .
That identity is true for only one of those values.
Did you leave some information out?

umm....nope...
i posted the question as it was given in my book...
what do you think will be the correct identity then??

**Plato** · February 9th 2010, 08:06 AM

Originally Posted by snigdha

umm....nope...
i posted the question as it was given in my book...
what do you think will be the correct identity then??

It is correct if $\theta\in I$ . Otherwise no.

**blackcompe** · February 9th 2010, 10:09 AM

Draw a 3-4-5 triangle where the hypotenuse is 5, the vertical segment is 4 and theta is opposite to it. Let theta = y. Therefore, siny is 4/5 and cosy is 3/5 Since tany = siny/cosy, tany = (4/5)/(3/5) or 4/3.

**snigdha** · February 10th 2010, 04:12 AM

Originally Posted by blackcompe

Draw a 3-4-5 triangle where the hypotenuse is 5, the vertical segment is 4 and theta is opposite to it. Let theta = y. Therefore, siny is 4/5 and cosy is 3/5 Since tany = siny/cosy, tany = (4/5)/(3/5) or 4/3.

But we are required to prove √(1-sin Θ)/(1+sin Θ) = 1/3
tanΘ = 4/3 is the information given to us....

**danielomalmsteen** · February 10th 2010, 04:19 AM

Hint :

$\sin \theta = \sqrt{1-\cos^2\theta} = \sqrt{1-\frac{1}{\sec^2\theta}} = \sqrt{1-\frac{1}{1+\tan^2\theta}}$

**snigdha** · February 10th 2010, 04:42 AM

Originally Posted by danielomalmsteen

Hint :

$\sin \theta = \sqrt{1-\cos^2\theta} = \sqrt{1-\frac{1}{\sec^2\theta}} = \sqrt{1-\frac{1}{1+\tan^2\theta}}$

wow!!

you are genius...!! how did you work this out..?!

i had spent almost 3days on this problem in vain..!!!

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