# Math

posted by .

the original problem was:
(sin x + cos x)^2 + (sin x - cos x)^2 = 2

I got 1 for (sin x + cos x)^2

but then what does (sin x - cos x)^2 become since it's minus?

• Math -

• Math -

(a+b)^2=a^2+2*a*b+b^2

(a-b)^2=a^2-2*a*b+b^2

[sin(x)+cos(x)]^2=
[sin(x)]^2 +2*sin(x)*cos(x)+ [cos(x)]^2

[sin(x)-cos(x)]^2=
[sin(x)]^2 -2*sin(x)*cos(x)+ [cos(x)]^2

[sin(x)+cos (x)]^2+[sin(x)-cos (x)]^2=
[sin(x)]^2 +2*sin(x)*cos(x)+ [cos(x)]^2+
[sin(x)]^2 -2*sin(x)*cos(x)+ [cos(x)]^2=
+[cos(x)]^2+[cos(x)]^2+[sin(x)]^2+[cos(x)]^2=
2*[[sin(x)]^2+[cos(x)]^2]=2*1=2

Becouse: [sin(x)]^2+[cos(x)]^2=1

• Math -

[sin(x)+cos(x)]^2=
[sin(x)]^2 +2*sin(x)*cos(x)+ cos(x)]^2

[sin(x)-cos(x)]^2=
[sin(x)]^2 -2*sin(x)*cos(x)+ cos(x)]^2

## Similar Questions

1. ### trig

Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The quantity …
2. ### tigonometry

expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b) …
3. ### Trig

Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos …

5. ### Mathematics - Trigonometric Identities

Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y …
6. ### TRIG!

Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 …
7. ### trig

The expression 4 sin x cos x is equivalent to which of the following?
8. ### 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 = - …
9. ### Trig

Find sin(s+t) and (s-t) if cos(s)= 1/5 and sin(t) = 3/5 and s and t are in quadrant 1. =Sin(s)cos(t) + Cos(s)Sin(t) =Sin(1/5)Cos(3/5) + Cos(-1/5)Sin(3/5) = 0.389418 Sin(s-t) =sin(s)cos(t) - cos(s)sin(t) =sin(-3/5)cos(1/5) - cos(1/5)sin(3/5) …
10. ### Trigonometry

Solve the equation for solutions in the interval 0<=theta<2pi Problem 1. 3cot^2-4csc=1 My attempt: 3(cos^2/sin^2)-4/sin=1 3(cos^2/sin^2) - 4sin/sin^2 = 1 3cos^2 -4sin =sin^2 3cos^2-(1-cos^2) =4sin 4cos^2 -1 =4sin Cos^2 - sin=1/4 …

More Similar Questions