SOLUTION: Prove each identity: tan^2(x)/1+tan^2(x) =sin^2(x) and sin^2(x)(1+1/tan^2(x))=1 i get confused for example sin^2(x) and (sinx)^2

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Question 1202859: Prove each identity:
tan^2(x)/1+tan^2(x) =sin^2(x)
and
sin^2(x)(1+1/tan^2(x))=1
i get confused for example sin^2(x) and (sinx)^2
Found 4 solutions by josgarithmetic, math_tutor2020, greenestamps, MathTherapy:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
Maybe you mean for your first one to be
tan^2(x)/(1+tan^2(x)) =sin^2(x)

or in the rendering tags

.

If you know or can find some specific identities you may see as possible step to begin

and then maybe you can continue to verify the rest of the way.


----
----




Distributive Property:

IDENTITY; proved
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

I'll prove the 1st identity and leave the other identity for the student to do.

LHS = left hand side
RHS = right hand side

I will transform the LHS into the RHS.
The RHS will be kept the same.



Use the identity 1+tan^2 = sec^2



Use identities tan = sin/cos and sec = 1/cos.











The identity has been confirmed.
Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!


Preliminary comments....

(1) "sin^2(x)" and (sinx)^2 are both used to represent the square of sin(x).

(2) Use parentheses properly. The first equation as you show it is not an identity:

tan^2(x)/1+tan^2(x) =sin^2(x) --->

The equation you intended to show is

tan^2(x)/(1+tan^2(x)) =sin^2(x) --->

Now my approaches to these....

Both of the other tutors used the identity 1+tan^2(x) = sec^2(x). That is certainly one way to start. But after that they turn everything into sines and cosines, so it seems easiest just to do that at the beginning.

(a)









(b)






Answer by MathTherapy(10557)   (Show Source): You can put this solution on YOUR website!
Prove each identity:

tan^2(x)/1+tan^2(x) =sin^2(x)

and 

sin^2(x)(1+1/tan^2(x))=1

i get confused for example sin^2(x) and (sinx)^2

Proving the left side equal to the right side!
            
                  ------ Substituting 
              ------ Substituting 
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