+4 Hi, I need help with the following questions!
1) Given that \(sin(x)+cos(x)=2/5\), what is \(sin^4(x)+cos^4(x) \)?
2) Simplify \(tan(15\pi/2)\).
3) Simplify\(\sqrt{(1-csc^2y)(cos^2y-1)}\).
4) Simplify \(\frac{sin(a)+csc(-a)}{cos(2\pi-a)-sec(a)}-cot(\pi-a)-cot(a)*csc^2(a) \).
5)Simplify\(\frac{sin(-a)*cos(a)+sin^2(-43^{\circ})+cos^2(-403^{\circ})}{cos(720^{\circ}+a)(sec(a)+csc(-a))}*\frac{sin^2(a)-cos^2(a)}{sin^3(a)+cos^3(a)}\).
Thanks in advance for the help!!
+128473 3) √ [ (1 - csc^2 y) ( cos^2 y - 1) ]
√ [ [ (sin^2y - 1) / sin^2 y] [ (-sin^2) ]
√ [ (sin^2 - 1) * (-sin^2 y / sin^2y) ]
√ [ (sin^2 y - 1) (-1)]
√ [ 1 - sin^2 y ] =
√ [cos^2 y] =
l cos y l
+128473 1)
sin x + cos x = 2/5 square both sides
sIn^2 x + 2sin(x)cos(x) + cos^2x = 4/25
(sin^2 x + cos^2 x) + 2sin(x)cos(x) = 4/25
(1) + 2sin (x) cos(x) = 4/25 subtract 1 from both sides
2sin(x)cos(x) = 4/25 -1
2sin(x)cos(x) = -21/25 divide both sides by 2
sin(x) cos(x) = -21/50 square both sides
sIn^2x cos^2x = 441/2500
sin^2 x ( 1 - sin^2x) = 441/2500
sin^2x - sin^4x = 441/2500
sin^4x = sin^2x -441/2500 (1)
sin^2 x cos^2 x = 441/2500
(1 - cos*2x) (cos^2x) = 441/250
cos^2x - cos^4x = 441/2500
cos^4x = cos^2x - 441/2500 (2)
Add (1) and (2)
sin^4 x + cos^4x = ( sin^2 x + cos ^2 x ) - 441/2500 - 441/2500
sin^4x + cos ^4 x = (1) - 882/2500
sin^4 x + cos ^4x = [2500 -882 ] / 2500
sin^4 x + cos ^4 x = 1618 /2500 = 809 / 1250
