1+sin x+cosx 1+cos x (b) 1+sinx-cos X sin x

Q: sinx 4 COS x cos*. COS x

A: In this question, the concept of Integration is applied. Integration Integration is a method of…

Q: secx-tan x cos x %3D 1+sin x secx+tanx

A: consider the left hand side of the equation sec x -tan xsec x +tan x sec x -tan xsec x +tan x=1cos x…

Q: cos( - x) = O sin( - x) O cos( + x) cos( - x) sin( + x)

A: The given expression is: cos π3-x Note that: cos θ=sin π2-θ

Q: 1- sin x cos x 1- sin x cos x

A: We can solve as follows

Q: c) cos x tan x = sin x tanx %3D (Usx.SinzL (os x Sinc sinx cot x + = csc x - CSC X 1+cos x (e Sinzx…

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Q: sin x 1-cos x = 2 csc x 1-cosx sinx

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Q: VERIFY THE IDENTITIES

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Q: (csc x- cot x)2 = 1- cos x %3D 1+ cos x

A: To prove: (csc⁡x−cot⁡x)2=1−cos⁡x1+cos⁡x We know that csx = 1sinx, cotx=cosxsinx

Q: 3. lim X-0 sinx sinx-cosx 4. lim x- 5. lim x(cosx-1) sinx-x

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Q: cosx sin'x = 3.. 3. cos°x sin°x= 5. = (sin°x- sin°x)cosx

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Q: sin(2x) cos(2x) Prove sec(x) sin(x) cos(x)

A: Trigonometry

Q: sin (x) – cos²(x) Show that 1 F COS %3D CSC (x)

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Q: sin x 1+ cosx 1+ cosx sin x 2cscx 2secx 01

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Q: Cotx-tanx=cos(2x)/sin(x)cos(x)

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Q: cos x - sec x = 0

A: Given equation can be written as Since secx=1/cosx Therefore, we have

Q: lim x----->0    sin x sin 2x/1- cos x

A: Given:-  limx→0  sinx  sin2x1-cosxTo find:-     value  of the above limit.Concept:-  Use 'L Hospital…

Q: Prove the identity. sin'x cos'x = (cosx-cos x) sinx 3. cos x- cos x) sinx

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Q: Use identities to simplify each expression.

A: cosxsin2x+cos3xsecx=cosxsin2xsecx+cos3xsecx=cos2xsin2x+cos4x…

Q: SIn (-x) In x if x 0

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Q: sin (3x) + cos (3x) cos(x) – =1+4sin(x)cos(x)

A: We use sin(3x)= 3sinx-4sin3x and cos (3x)= 4cos3x-3cosx .

Q: sinx-cos x 1. tan x cscx-secx cot x sin x coS X %3D

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Q: sin x 1+cosx 2csc x= 1+cos x sinx

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Q: sin 2x 29. sin x cos 2r = sec x cos X

A: As you mentioned solve question no.29

Q: sin 2x 4. tan x = %3D 1+cos 2x 19 5. tan %3D = CSC X - cot x

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Q: sin x 1+ cosx 1+ cosx + sin x 2cscx 2secx 01

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Q: (sin x + cos x) sin'x- cosx sin'x- cos'x cos-r COS X (sin x – cos x)2

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Q: 1+sin x/cos x + cos x/1 + sin x = 2 sec x

A: Given:1+sinxcosx+cosx1+sinx=2secx

Q: inx-cosx -= sin x cos x сх-sec x сot х 1 cotx cscx+cotx tanx < – sin*x = 1 – 2 sin² x cot x sin x…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: sin x COsx Prove 2tanx secx - - cosx 1+ sin x

A: We use the identity sin2x + cos2x=1

Q: 1- cos () 1- cos(x) 1- sin°(;) 1+ cos(x)

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Q: 8 sin x cos x sec x =

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Q: 1+ cos(x) sin(x) 1+ cos(x) = 2 csc(x) sin(x)

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Q: 1+ cos x 2. 1 - cos x (csc x+ cot x)2

A: L.H.S :    1+cos x1-cos x               =(1+cos x)(1+cos x)(1-cos x)(1+cos x)               =(1+cos…

Q: sin 2x+sin x dx Vsin2x -cos x v.

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Q: sin 2x cos x + cos 2x sin x = −1

A: sin(x+y)=sin(x).cos(y)+cos(x).sin(y) if sin (θ)=-1       then  θ=(2nπ+3π/2)  where n is an integer

Q: . sin 2x cos x+ cos 2 sin x = 12

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Q: sin 3x-sin x Prove tan x. cos 3x+cos x

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Q: (Sin X-cos X)^2=1-sin 2x

A: Formulae to note: (a-b)2=a2+b2-2ab. 2 sin x cos x=sin2x. Sin2x+Cos2x=1.

Q: 1) f(x) = x5-x¹ + x² - x +² 2) f(x) = sin³x - e³x² + ln(1 + 5x²) 3) f(x)=√1-x² sin-¹ x 4) f(x)=√√x +…

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Q: cos4x - sin4x = cos 2 x 2 cos 2 x -cos 2 x

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Q: sin^2 x + sin x cos x over cos x − 2 cos^3 x

A: This question is based on Trigonometric Formulas to simplify question.

Q: COs x + sinx COS x - Sln x - sin = 2 tan 2x %3D Cos x- sin x COS x + sin x

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Q: 1- Sinx+ Sin'x 4 X. 2 1-Cosx+Costx 1- Sin'x (1- Sin²x) (x, 1-Cos'x (1-Cosx)

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Q: sinx + sin 2 Evaluate | cosx A. -In cos x|– x+ C В. In'secx-x+ C C. -In|sec x|+ x+C D. In sec x|+x+C

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Q: sin(3x)-sin x - cot(2x)= cos(3x) - cos x

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Q: sin x cos x 1 1. - sin – sin x 2 sinx cosx 3 cosx -1

A: The solution is given as

Q: Sin (3 x) Sin (3 x) dx

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Q: cos2x – sin2x cos2x - -F(x)+C. What is F(X}? For dr =- 3 cosx – sinx -

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Q: ( (cos (2x) – sin(2x) cos( 2x)) cos (x) – sin(x) For (x) +C. What is F (x)?

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Q: 5.) cos (x -) + sin ( – x) = cos x cos (x -) + sin ( - x) = 3

A: Since multiple questions are asked, according to guidelines answering first question. Cos60 =1/2…