2. Prove sec?x + tanx secx 1- sin x

Q: 5) Prove that tan(x) + cot(x) = [sec(x)][csc(x)]

A:

Q: (A) Verify the identity (i) (1 + tan² x)(1 - sin2x) = 1 sec x - 1 %3D tan x (ii) tan x sec x + 1 1+…

A: We have to prove the identities.

Q: tan? x sec² x + secx Prove -cos x

A:

Q: Prove that the inequality sinx+tanx>2x holds in the interval (0,π/2).

A:

Q: A. PROVE THE FOLLOWING IDENTITIES: 3. tan*x + tan²x = sec*x – sec'x tanx+secr-1 1+sinx tanx-secr1…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Verify the identity: 1- sin(2x) 1- tan x cos(2x) 1+ tan x

A: LHS: 1-sin(2x)cos(2x)=cos2x+sin2x-2sin(x)cos(x)cos2x-sin2x ( as…

Q: 2 Using the relation 2 (1 cosx) x, V x € (0, - · 4)

A: A relation is given by, 21-cosx < x2, where x≠0. The objective is to use the given relation to…

Q: Q2. Prove that sec2(tan-x) = 1+ x?

A:

Q: Prove the identity. secx- cosx sinx tanx

A:

Q: Prove the identity. sin x+ 2. = cotx sin (n-x)

A:

Q: 1 Verify the identity 1 = 2 tan x sec x %3D 1-sin x 1+sin x

A:

Q: If z = tan X 2 then sin x =

A:

Q: 4. Verify the identity: (sec 0 + tan 0) (sec 0 – tan 0) = 1

A:

Q: Evaluate / 5 sec2 *dx tan(x) 05 In(|tan(x)|) + C Oln(tanx) + C 05 In(x) + C 05 tan(x) + C

A:

Q: cosx tanx In(1+x)

A: Write the power series in sigma notation and in expanded form

Q: Prove the identity. secx- sin x tanx= cosx

A: Given,          secx-sinxtanx=cosx

Q: Using suitable method, show that 2 tan" (x+2) dx =- – In 2 .

A: We use integration by parts to find integral tan inverse x.

Q: HW/Prove that: . (1) tanx=cot! tan"x= cot-1 (2) sin x = csc -11. (3) sin (sin x) = x

A: We have to prove the identities 1. tan-1x=cot-11x2. sin-1x=csc-11x3. sin-1sinx=x

Q: 2. Verify: sin x+tan x %3D sin2x sec x cscx+cotx

A:

Q: Prove the identity: sin (x-y) tanx- tany cosx cosy

A:

Q: Prove that ? 2tan X tan 2X 2 1-tan x

A:

Q: (a) Show that tan x = dx sec?x using quotient rule.

A:

Q: Q4: Prove that: secx • cscx = tan x + cot x

A: According to guidelines we should have been able to solve only one question at a time #4

Q: 24: Prove that: secx * cscx = tan x + cot x

A: To prove the given identity

Q: provethat 2. 1- cosx +Sin'x

A:

Q: HW/ Prove that: (1) 1-tanif x sechx

A:

Q: 2. Verify: sin x+tan x %3D sin?x sec x cSc x+cotx

A:

Q: * tan°(x) cos“(x) 1 tan7(x) 1 tan (x) O tan7(x),

A:

Q: tan x 3. = sin x %3D secx

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: Verify the identity 1- sin x (sec x- tan x)2 = %3D 1+sin x

A: secx-tanx2=1cosx-sinxcosx2=1-sinxcosx2=1-sinx2cos2x=1-sinx21-sin2x…

Q: Prove the identity.   (1-tanx)^2=sec^2x-2tanx.

A: We have to prove the identity(1-tanx)2= Sec2x - 2 tanx

Q: Prove that the inequality sinx+tanx>2x holds in the interval (0,π2).

A:

Q: | tan° xsec* xdx 6 2. Use 1 + tan² x = sec? x to evaluate

A: Solution:

Q: Prove tan x + cos x = sin x (sec x + cot x).

A: We have to prove the identity: tan x+cos x=sin x sec x+cot x We know the relation between…

Q: 6) Verify tan x + cot x = sin(2x)

A: Simplification

Q: 3) Prove that b) tan- (*)} = sechx

A: Evaluate the derivative of the given function as follows. ddxtan-1ex=11+ex2ddxex…

Q: Prove that? 2tanX tan 2X %3D 2 1- tan x

A: Given : 2tanx1-tan2x = tan2x

Q: Prove the identity. tan x tan sec x + 1 2.

A:

Q: Prove the identity 1÷(1-sinx) =sec^2 x +tanx secx

A: 1(1-sinx)=sec2x+tanxsecx

Q: Prove the identity. cos x- secx=-sinx tan x 2.

A:

Q: Prove the identity. sec(-x)-sin(-x)tan(-x)=cosx

A: sec(-x)-sin(-x)tan(-x)=sec(x)-(-sin(x))(-tan(x))=sec(x)-sin(x)tan(x)

Q: Prove sin 2  x/2=  tan x - sin x / 2 tan  x

A: The given identity is sin2x2=tanx-sinx2tanx

Q: Prove the identity Sinx/1-cosx=secx+1/tanx

A:

Q: Prove that 2 Sin X dx 1 + cotx + cos x It tan X cos 2 x

A:

Q: Prove that _ d tanx = Sec'x.

A:

Q: prove  cosx( 1- tan x)= cos x- sin x

A:

Q: Prove the identity : sin(x-y) tanx- tany Cosxcosy

A: Consider, tanx-tany=sinxcosx-sinycosy=sinx cosy-cosx sinycosx cosy=sinx-ycosx cosy…