Verify the identity. (Simplify at each step.) sin1/2 x cos x - sin5/2 x cos x = cos³ x/ sin x sin /2 x cos x - sin5/2 x cos x (V ainx)cos (1 sin x )cos X = cos3 x/ sin x

Q: Which expression is equal to cos(6t)?

A: Recall:  cos(2t)=cos2(t)-sin2(t)     Given,   cos(6t)

Q: epresent 3 sin x + 6 cos x in a form A sin(x + p), use radians for p.

A:

Q: Find an alternative form in terms of x for each of cos(sin- 1 x) and tan(sin- 1 x).

A: Let us make a triangle with opposite = x and hypotenuse=1 , because sin theta= opposite/hypotenuse…

Q: Rewrite cos x + 3 in terms of sin(x) and cos(x). COS

A:

Q: Verify the identity: sin x/(1 + cos x) = (1 - cos x)/sin x.

A: sinx1+cosx=sinx1+cosx×1-cosx1-cosx=sinx1-cosx1-cos2x     ∵a+ba-b=a2-b2=sinx1-cosxsin2x…

Q: sin4x sin2x=1/2(cos2x-cos6x). Prove the identity

A: Consider the given identity

Q: s 4

A: To simplify (cos 3x)(cos x)-(sin 3x)(sin x)

Q: Simplify. cos(-4x) · cos 2x – sin(-4x) · sin 2x cos(-2x_ sin(-6x) cos(-3x) cos(-x)

A: Using Cos(A+B) formula

Q: Verify identity cos2 x - sin2 x = 2 cos2 x - 1.

A: cos2x -sin2x=2cos2x-1

Q: Verify the identity: [sin 2x + (sin 3x + sin x)]/[cos 2x + (cos 3x + cos x)] = tan 2x

A: Consider the identity, sin2x+sin3x+sinxcos2x+cos3x+cosx=tan2x To apply the trigonometric identity,…

Q: Rewrite cos ( x –) in terms of sin(x) and cos(x) 3

A: we know that cos(x-y)=cos(x)cos(y)+sin(x)sin(y)