a) By expanding sin (2x + x) and using double angle formulae, show that sin 3x = 3 sin x- 4 sin'x. Hence, prove that sin'x dx = 24 %3D |

Q: Use a calculator to compute sinhx and coshx for x = -3, 0, 5.

A: We use a calculator to find the values.

Q: ܤܡܪܝܢ ܐ 2 6. The value of [sin' xdx is 0

A:

Q: Is (1-sin x) not the same as (sin x - 1)?

A: (x - y) is not same as (y - x), whereas  (x - y) = - (y - x)

Q: What is the general solution for 1 + sin(2x) = sinx?

A: To find the general solution for the equation 1+sin⁡(2x)=sin⁡(x), it can use trigonometric…

Q: Then use equation (1) to find sin'x cos5x 0 -dx.

A: Given integral ∫0π4sin7xcos5xdx

Q: x+(1/x)=2 cos theta , then show that x2+(1/x2 )=2 cos2 theta

A:

Q: Differentiate  (sin(x+a)/cosx)

A:

Q: Prove: Sin(x-pi/2) = -cosx

A:

Q: 1. If z = sin2+In^, find the value of x- +y X

A:

Q: Consider the function y=sin0, where 0=u+v. Suppose that u = v. Show how the Sum and Difference…

A: We will see the ans in next step

Q: 2. Is trigonometric substitution needed to evaluate /9 - x² dx?

A:

Q: 1-sin' x 3D sin.x 6. cosxcotx

A:

Q: We know that a= 23 sin' (ax) cos(ax) dx = sin³ (ax) b Find b + C

A:

Q: Prove that: Sin'x+ cosx=I

A:

Q: Verify the identity cosh 2x = cosh2 x + sinh2 x

A: we have to verify the identity: cosh(2x)=cosh2x+sinh2x   L.H.S: cosh2x as we know that coshx=ex+e-x2…

Q: Differentiate y = 5 sin(2x-4). O a) dx = = -5 sin(2x-4) о O b) ad ax O c) = 5 cos(2x-4) = -10 sin(2x…

A:

Q: Find sec2x if sin x = 6/10 and sec x < 0

A:

Q: If 2 sin-' p = cos-q, show that 4p² – 4pª + q° = 1.

A:

Q: D FLx)= sSine? do 3.

A:

Q: Evaluate sin" a cos a da.

A: Given : ∫sin4x cosx dx

Q: sin'x cos'xdk 3. X COS

A: It is given that, ∫sin2xcos3x dx We have to solve it.

Q: :: Evaluate: S sin 2x sin x dx 1/3 sin'x + c 1/3 sin'x +c 2/3 sin'x + c d. 2/3 sin'x +c a. с. b.

A: Given: ∫sin(2x)sin(x)dxWe know that sin(2x) =2sin(x)cos(x)Then…