2 To evaluate the integral (384 + 576 sin(t) + 216 sin (t)) dt, we recall the trigonometric identity,

Q: Find sin π/4, cos π/4, and tan π/4.

A:

Q: 5. Find the values of a and b such that dx tan 1 + sinx a + b . %3D

A: We need to integrate ∫11+sinxdx

Q: 2 sin-√3 = 0, [0°, 360°) 2

A:

Q: Solve the equation sin 0 + 3 cos 0 = 1 for 0€ [0, 2л).

A: Explained below

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: Which is the exact value of the trigonometric expression sin 2-2 F H 2+ 1+ G J 2. 2. 2.

A:

Q: ow that the equation 2x – 1– sin x 0 has exactly one real root.

A:

Q: Ex2: Use the identities 4 and 5 to prove that: cos(x- y)-cos(x+y) (a) sin x sin y = 2

A: Formula used -  cos(A-B) = cosA cosB + sinA sinB  cos (A+B) = cosA cosB - sinA sinB

Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

A:

Q: cos e de sin² 0 + 4 sin 0-5

A: To evaluate the given integral.∫cos θ dθsin2 θ+4 sin θ-5

Q: sin? cos' dx 2.

A:

Q: 2 Cos4 Sin (sinz) de

A: Consider the integral  ∫cosxsin2sinxdx

Q: Verify the identity (sin x + cos x)² = 1+ sin 2x by converting the left hand side to the right. Give…

A:

Q: Verify the identity: sin (3π/2 - x) = -cos x

A: To prove  sin (3π/2 - x) = -cos x

Q: Show sin 3A = 3 sin A cos²A - sin A.

A: Explanation: Given that: sin3A=3sinAcos2A-sinA Concept: sin3A=3sinA-4sin3A sin2A+cos2A=1

Q: Evaluate | sin2x tan (sinx)dx

A: