Calculus

posted by .

Solve identity,
(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 -

First 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 -

Cross 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 -

Got it, thanks!

Similar Questions

1. trig

sinx = 4/5 and x terminates in Quadrant II Find sin2x and cos2x How to get the answers, which are sin2x = -24/25, cos2x = -7/25?

Solve the equation of the interval (0, 2pi) cosx=sinx I squared both sides to get :cos²x=sin²x Then using tri indentites I came up with cos²x=1-cos²x Ended up with 2cos²x=1 Would the answer be cos²x=1/2?
3. Calculus II

How does one obtain cos2x = cos^2(x) - sin^2(x) by differentiating the identity sin2x = 2sinxcosx

solve for (<_ = less than or equal to / pie = pie sign / -pie = negative pie) 3 sin²x = cos²x ; 0 <_ x < 2pie cos²x - sin²x = sinx ; -pie < x <_ pie
5. trig

write sin4xcos2 as the sum or difference of two functions. answers: 1/2(cos6x+cos2x), 1/2(cos2x-cos6x), 1/2(sin6x+sin2x), sin6x-sin2x
6. trig

write sin4xcos2 as the sum or difference of two functions. answers: 1/2(cos6x+cos2x), 1/2(cos2x-cos6x), 1/2(sin6x+sin2x), sin6x-sin2x
7. trig

write sin4xcos2 as the sum or difference of two functions. answers: 1/2(cos6x+cos2x), 1/2(cos2x-cos6x), 1/2(sin6x+sin2x), sin6x-sin2x
8. trigonometry

Been trying this forever so it says: Simplify 1+sin2x+cos2x/1+sin2x-cos2x ive tried this problem so many times I need help with it...
9. maths

prove that 1+sin2x-cos2x / sin2x+cos2x = tanx
10. Maths

Prove that sin2x+cos2x-1/sin2x+cos2x+1=tanx

More Similar Questions