Evaluate sin (ax + 6) dassuming that a and b are constants and a 0 O cos (az | b) C O cos (az + b) 0cos (az - b)+C cos (ar + b)+C.

Q: Prove the identity. 10 10 + = 20 sec %3D 1- sin x 1+ sin x

A: Take lcm and then solve

Q: sin? x 1- 1-cos x =-COS X

A: Here we have to use the basic trigonometric identity sin2θ+cos2θ =1 and we know that  a2-b2=…

Q: Find the expression , identical go Cat (9x) the given a. sin 46x) - sinx Cos x - sin(16x) b. cos…

A: Expression of cot(9x) : See all the options And use the trigonometric formula .

Q: 2 Simplify completely: sec x (1 – sin² x). sec x CO X O None of these. O 1 sin x

A: we use Trigonometry identities

Q: Verify the identity. csc(x) cos²(x) + sin(x) = = = csc(x) cos²(x) + sin(x) = csc(x) 1 sin(x) 1 2…

A: Given csc(x)cos2(x)+sin(x)=csc(x)

Q: 5) cos A 30 B 16 34 7) sin Z 32 40 24 x, 9) cos Z 24 30 x,

A:

Q: Write the expression -/3 sin x + cos x in terms of Sine only, in the form k sin (x + 4). Select one:…

A: Explanation: Given that,  -3sinx+cosx     Formula used:…

Q: Prove the identity. Cos(x− 90°) − Cos( x + 90°) = 2 sin x

A: We will use the formulas: cos(A-B)=cosAcosB+sinAsinBcos(A+B)=cosAcosB-sinAsinB

Q: Prove the identity. sec2 (x/2)= 2 sec x + 2/sec x + 2 + cos x

A: The given equation is,

Q: Expand and simplify: sin(x+3)-cos(+ x) 6 COS X

A:

Q: 48. Simplify a. 1/cos x b. 1/secx c. 1/tan x d. 1/sin x 1 sin³ x col² x sin x

A:

Q: Rewrite – 6 sin(2) + 3 cos(x) as A sin(x + ¢)

A: Given data:   The given expression is -6sin(x)+3cos(x).   The given expression can be written as,…

Q: proof 1)  (sin x + cos x)2 = 1+ 2 . sinx . cosx 2)  cos4x - sin4x = cos2x - sinn2x

A:

Q: 2 cos I Use a counter-example to show that cos 2x

A:

Q: Evaluate [sin2xcos2x, dx 1 Acos4x+C 1 ® - cos4x+C B 1 -cos4x + C Cos 1 -cos4x + C

A:

Q: Derive/Prove: sin 2x = 2sin xcos x Useful Formula: cos 2x = cos?x-sin? x a. = 2 cos x-1 =1-2sin x…

A:

Q: Prove sin?x tan²x – cos?x = sec²x - 2

A: To prove : sin2x tan2x - cos2x = sec2x - 2

Q: Verify the identity. (Simplify at each step.) cos³ x sin“ x = (sin“ x – sin x)cos x cos x sin“ x =…

A: Using First Identity Of Trigonometry.

Q: Rewrite in terms of sin(x) and cos(x) cos(x-5pi/

A: GivenCos x-5π6

Q: 5. cos A =- and sin B =, both A and B in QIl. 6. cos A = - and cos B = - 2, with A and B in QIII. 17

A:

Q: a. [CO²2 2 cos²x√4 tan x tan² x da

A:

Q: 6. Prove that: ah cos (i) A sin (ar + b) = 2 sin (ah sin a (ii) A cos (ar + b) = - 2 sin

A:

Q: Evaluate. V3 sin 士 %3D 2 + = [Select] a = [ Select ] b = [ Select ]

A:

Q: Q/prove that : (cos x) = -Sin X %3D

A:

Q: Verify the identity. 1 + sin 2x cos x+ sin x %3D cos 2x cos x- sin x Choose the sequence of steps…

A: Sin2x correct formula is- Sin2x=2SinxCosx So this formula is only used in option 2

Q: Prove the identity. cos(x + y) + cos(x – y) = 2 cos(x) cos(y)

A: It is given that,

Q: Prove: sin? x 2 cos“ = cos 2-2cos x

A: We will use basic properties of trigonometric ratios

Q: Simplify. 1+ sin 2x+ cos 2x COS X O A. 2(sinx+ cos x) O B. 2 tan x O C. 2 cot x O D. 2(sin x- cos x)

A: We have to silmplify

Q: Evaluate sin (ax) (ax) V3 (2ах) da Cos

A:

Q: Verify the identity. (Simplify 3 cos x 3 cos y sin x + sin y 3 cos x at each step.) sin x + sin y +…

A:

Q: A) How does 1/2[(1-cosx)/(sinx)+(sinx)/(1-cosx)] equal on of these: secx, cosx, sinx, tanx, cotx,…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: sin ²e + cos²e =(1)". if n>1

A:

Q: (7cosx-sinx)2 + (cosx+7sinx)2 = 50 Verify the identity.

A: Given,

Q: cos ax dx = xe", a 2 0. (or) Evaluate x' +1 cos ax 2: Prove that x +1

A:

Q: Verify the identity. cos (x+ n) = - c COSX

A: It can be varified using the formula for cos(A+B)

Q: Multiply and simplify. (Show your work) (cos x - sin x) 4 O cos-x + 2 sinx x cos>x- +2 sin x- COS X-…

A: To multiply and simplify cosx-sinx2

Q: Rewrite cos(x+11π6)cos(x+11π6) in terms of sin(x)sin(x) and cos(x)cos(x)

A: Given expression is cosx+11π6

Q: Verify the identity (1+sin x)(1-sin x)=cos2x   (sin x + cos x)2 + (sin x - cos x)2=2   cot(x) =…

A: (1+sin x)(1-sin x)=cos2x Apply FOIL method to expand left side

Q: Verify the identity. (Simplify at each step.) .3 cos x sint x = (sin x sin x)cos x cos³ x sin4 x =…

A: The solution is given below in the next step:

Q: Prove that ²-1 (²) (0) (sin (+,-) + do r² sin(0)

A: Given : ∇2=∂2∂x2+∂2∂y2+∂2∂z2 To Prove : ∇2=1r2∂∂rr2∂∂r+1r2sinθ∂∂θsinθ∂∂θ+1r2 sin2θ∂2∂ϕ2

Q: Verify the identity: cos4 t - sin4 t = 1 - 2 sin2 t

A: We have the identity cos4t-sin4t=1-2sin2t   Consider LHS LHS=cos4t-sin4t Rewrite as…

Q: tan(x) – cos²(x) dx Evaluate: cos(x) A sec(x) -sin (х) +с B B sec(x) + sin(x) + C © sin(x) – sec(x)…

A: We can find the integration as below

Q: Rewrite -6 sin(æ) - 3 cos(x) as A sin(x + 4)

A:

Q: (a). Find a common denominator for COSX |- COSX and 1- COS x COS x –COS X COSX = cosx-coseX COS X…

A: a To find a common denominator for 1cos x and cos x1-cos x.b To expand cos x+tan x2 and to simplify.

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

A: we have to verify the identity : cos(x+h)-cosxh=cosx(cosh-1)h-sinx(sinh)h

Q: Prove the identity. 3 sin(x – y) cos y cos x 3 tan x - 3 tan y

A: Given that  3tanx-3tany=3sin(x-y)cosycosx We need to verify the given identity.

Q: 5. Does cos(x) = x³ have a solution? Explain. %3D

A:

Q: Rewrite sin(x+7π4)sin(x+7π4) in terms of sin(x)sin(x) and cos(x)cos(x)

A: Given: sinx+7π4 To find: Rewrite in terms of sinx and cosx.   Required formula:…

Q: Solve r-t cos x+p tan x = 0, %3D

A: The solution is given as

Q: sin(3x)cos(3x) sin(2x) 의[cos(2x)-1]+ +C 12 8 4

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.