Trigonometrical Identities and Simple Equations

[wanchosen]

Hi there, I am struggling with trigonometrical identities and how to use them effectively. I can work out simpler problems but I can't seem to get my head round slightly bigger ones like this:-

Simplify:-

sin^4(x) + 2sin^2(x)cos^2(x) + cos^4(x)

I 've tried substituting "2sin^2(x)cos^2(x)" with

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

and also tried

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

but end up going round in circles. Can somebody give me some pointers please!

Thanks!

 

[Curious3141]

sin x = s, cos x = c

Hint : s^4 + 2s^2c^2 + c^4 = (s^2)(s^2) + (s^2)(c^2) + (c^2)(s^2) + (c^2)(c^2).

Collect the terms and see what you come up with.

 

[Vagrant]

Sin^2x + cos^2x =1

 

[Kurdt]

As Curious has hinted this has been cleverly constructed to be a quadratic in trigonometric functions. It should be quite easy to solve now.

 

[wanchosen]

Thanks for that! Must remember to factor! That made it easier to solve.