# Trig

posted by .

simplify the expression to a single term:

(1-2Sin^2 X)^2 + 4sin^2 X Cos^2 X

I'm not sure how to start this or which identities to use. Any suggestions?

• Trig -

(1-2Sin^2 X)^2 + 4sin^2 X Cos^2 X
(sin^2 x + cos^2 x - 2sin^2 x)^2 + (2sinxcosx)^2
= (cos^2x - sin^2x)^2 + (sin 2x)^2
= (cos 2x)^2 + (sin 2x)^2
= 1

## Similar Questions

1. ### trig

2sin(x)cos(x)+cos(x)=0 I'm looking for exact value solutions in [0, 3π] So I need to find general solutions to solve the equation. But do I eliminate cos(x), like this... 2sin(x)cos(x)+cos(x)=0 2sin(x)cos(x)= -cos(x) 2sin(x) = …
2. ### math

how would you find the angle to (3)^.5sin(2x)-2cos(2x)+2sin^2(x)=1 I know that you have to use the trig identities but then when i substitue the sin and cos(2x) in i don't know what to do. please help
3. ### trig

I need to find all solutions of the given equations for the indicated interval. Round solutions to three decimal places if necessary. 1.) 3sin(x)+1=0, x within [0,2pi) 2.) 2sin(sq'd)(x)+cos(x)-1=0, x within R 3.) 4sin(sq'd)(x)-4sin(x)-1=0, …
4. ### Precal

I do not understand how to do this problem ((sin^3 A + cos^3 A)/(sin A + cos A) ) = 1 - sin A cos A note that all the trig terms are closed right after there A's example sin A cos A = sin (A) cos (A) I wrote it out like this 0 = - …
5. ### trig 26

simplify to a constant or trig func. 1. sec ²u-tan ²u/cos ²v+sin ²v change expression to only sines and cosines. then to a basic trig function. 2. sin(theta) - tan(theta)*cos(theta)+ cos(pi/2 - theta) 3. (sec y - tan y)(sec y + …
6. ### Trigonometry

Solve. 2sin(2ƒÆ) + ã3 = 0 interval [0, 2ƒÎ) How do I start this?
7. ### trig

2sin(4x)[(cos(3/2)x)(cos(5x/2)-sin((15/4)x)]+x can someone simplify this using trig identities?
8. ### Precalculus

Verify the identities. Cos^2x - sin^2x = 2cos^2x - 1 When verifying identities, can I work on both side?
9. ### Trigonometry

Factor the expression and use the fundamental identities to simplify. 1-2 cos^2x + cos^4x
10. ### Trig identies, Calculus

Use the identities cos^2 x + sin^2 x =1 and cos2x=cos^2 x -sin^2 x to show that cos^4 x -sin^4 x = cos2x Im not sure how, I can solve my problem with half angle identities but im not sure where to start with this.

More Similar Questions