Thursday

July 24, 2014

July 24, 2014

Posted by **sh** on Saturday, February 27, 2010 at 11:22pm.

(1-sin2x)/cos2x = cos2x/(1+sin2x)

I tried starting from the right side,

RS:

=(cos²x-sin²x)/(1+2sinxcosx)

=(cos²x-(1-cos²x))/(1+2sinxcosx)

and the right side just goes in circle. May I get a hint to start off?

- Calculus -
**Reiny**, Saturday, February 27, 2010 at 11:51pmFirst of all since the angle is 2x throughout, let's just use y for 2x

Secondly, you probably want to prove it as an identity, rather than solve it

RS

= cosy/(1+siny)**[(1-siny)/(1-siny)]**

= cosy(1-siny)/(1- sin^2 y)

= cosy(1-siny)/cos^2y

= (1-siny)/cosy)

= (1- sin 2x)/cos 2x

= LS

- Calculus -
**drwls**, Saturday, February 27, 2010 at 11:51pmCross multiply.

cos^2(2x) = 1- sin^2(2x) = cos^2 2x

q.e.d.

x can be anything.

That is why it is called an identity

- Calculus -
**sh**, Sunday, February 28, 2010 at 12:00amGot it, thanks!

**Related Questions**

Calculus II - How does one obtain cos2x = cos^2(x) - sin^2(x) by differentiating...

pre-calc - Solve: cos(2x-180) - sin(x-90)=0 my work: cos2xcos180 + sin2xsin180= ...

calc - Where do I start to prove this identity: sinx/cosx= 1-cos2x/sin2x please ...

Trig....... - I need to prove that the following is true. Thanks (2tanx /1-tan^x...

Math - Calculus - The identity below is significant because it relates 3 ...

math - Prove the identity: 1-cos2x/sin2x = 1+tanx/1+cotx I simplified the RS to ...

Math - Solve this equation algebraically: (1-sin x)/cos x = cos x/(1+sin x) --- ...

math - Can anyone help w/ these. 1) Solve the equation in the internal [0deg, ...

trig - it says to verify the following identity, working only on one side: cotx+...

math - How would you establish this identity: (1+sec(beta))/(sec(beta))=(sin^2(...