Prove the identity cot (x)+tan n(x)%3Dsec(x)csc (x)

Q: Prove the identity. cos (x+y) =1- tanx tany cosx cosy

A: Given L.H.S is cos(x+y)cosx.cosy We know that cos(a+b)=cosa.cosb-sina.sinb substituting the formula…

Q: Prove the identity. cos(x-y) / cosx cosy = 1+tanx tany

A: To Prove:cosx-ycosxcosy=1+tanxtany

Q: 11. Prove the identity sin x 1+ cos x 2 csc x 1+ cos x sin x

A:

Q: Verify the identity: (sin x - sin y)/(sin x + sin y) = tan (x - y/2 cot (x + y)/2

A: We will use the formulas

Q: Verify the identity: sin(x - y)/(cos x cos y) + sin(y - z)/(cos y cos z) + sin(z - x)/ (cos z cos x…

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Q: Evaluate lim cos(n+sin x)

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Q: If y = sin x, then y' = - cot x sin x - tan x sec x sec x -sin x - Cs X tan x cos X CSC X

A: Given function is y=sinx. Differentiating the given function with respect to x, we get…

Q: verify the identity: sin(x+y) + sin(x-y)         = tanx cos(x+y)+cos(x-y)

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Q: Prove the identity. cosx 1- sin x 1 = tan x cos x

A: We need to prove the following identity cosx1-sinx - 1cosx = tanx

Q: Evaluate sin(x) 1+cos(x) -dx

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Q: 1 Let f(x) (5 sin x + 4 cos x æ)tan- f'(x) =

A:

Q: Prove the identity.   (cosh x + sinh x)n = cosh nx + sinh nx  (n is any real number)

A: The cosh x and sinh x are given by, LHS =

Q: Prove the identity. tan(x -)- -cot(x) TC tan x 2 %3D sin(x - ) | tar(x-)- sin(x) cos) - cos(x) sin…

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Q: Prove the identity. sin(x+y) sinx + cos(x+y) cosx = cosy

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Q: Prove the identity. cos (x+y) 1- tanx tany cosx cosy

A: We need to prove the following identity cosx+ycosx cosy = 1-tanx tany

Q: Prove the identity. sin'x cos'x= (cos'x- cos"x) sin x

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Q: cos(x – y) Prove that tan y + cot x sin x cos y

A: We need to prove cosx-ysin x cos y=tan y+ cot x                  Now, we will use the formula…

Q: Prove the identity. cosh(x) + sinh(x) = e* cosh(x) + sinh(x)

A: The solution of the problem is given in the next step.

Q: 3-f(x) = tanh¯1(cos(e*))

A:

Q: Find y': COS X y = 1-sin x O y' = sin² -sin x-cos² x (1-sin x)²

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Q: Verify the identity: (tan x + tan y)/(1 - tan x tan y)= (sin x cos y + cos x sin y)/ (cos x cos y -…

A: Given: verify that tanx+tany1-tanxtany=sinxcosy+cosxsinycosxcosy-sinxsiny for verifying given…

Q: 24. Prove the identity sec(x) (sin(x) + cos(x)) sec(x) + 2 sin(x)

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Q: Evaluate (tan x cos x) dx А. cos x + C cos x + C - С. - sin x + C D. sin x + C B.

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Q: tan x 4. a) Evaluate dx. In (cos x) b) Evaluatef e4*x3 dx.

A:

Q: tan x 2. (a) lim e →号一 (b) lim sin (tanh 3x) エ→十0

A: limx→π2-etanx

Q: Show that the two formulas are equivalent                                                      ∫tan…

A: To show that ∫tanx dx=-lncosx+C and ∫tanx dx=lnsecx+C both formula are equivalent. We know that…

Q: Evaluate: / [cos(x) – sin(x«) ]dr A cos(x) + sin(x) +C - cos(x) + sin(x) +C

A: In this question we will use basic of calculus i.e concept of integration. We will simply use the…

Q: Prove the pollowing identity.. (sin x t cos L cas x)- sin 2X-CoS T Sin'x + Cosx

A:

Q: Verify the identity: sec x - 1 = sec x 1- cos x

A: Now , we will verify the identity.  We know,  1/cosx = secx .

Q: tan x - X 1. lim sinx 5 A. 2 В. 2 С. О D. undefined

A:

Q: Prove the identity. s (xxy) sinx- sin (x-y) cosx= siny cos

A:

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

A: To prove  sin (3π/2 - x) = -cos x

Q: 3. Prove the identity tan * COS v t CSC x Sinx=2sinx

A: Prove the identity

Q: Prove the identity. V3 + tan(x) tan(x + ) - 1- V3 tan(x)

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Q: Prove the identity. TC cos = tanx %3D cos (T+x)

A: To Prove:

Q: Prove the identity  cos(x+y)/cos x * cos y = 1- tan x * tan y

A:

Q: Prove the identity. sin(n-x)сos(n+x)tan(2π − x) T 3π 3π sec+ x)csc(³7-x)cot (³7 + x) = sin^x - sin²x

A: I have appended the formula used in the solution part of the question

Q: Prove the identity. sin x 1+ cos x 1- cos x sin x

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Q: Prove the identity. cos (x+y) = 1 - tanx tany cosx cosy

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

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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: Evaluate (sin² (sin² x cos x)(1+ sin z cos x) dx.

A: Use substitution method

Q: • tan°(x) Xp- cos“(x) 1 1 tan9

A:

Q: Prove the identity.  cosh x - sinh x = e -x

A: Consider the given identity of L.H.S as coshx-sinhx

Q: Verify the identity. 1- sin x + COs X 1 + sin x + cos X COS X | sin x + 1

A:

Q: Find sin (x/2) cos(x/2) tan(x/2)

A: Given information is :

Q: Prove the identity.   sinh(x+y) = sinh x cosh y + cosh x sinh y

A: To show that sinhx+y=sinhx coshy+coshx sinhy

Q: S [tan® x sec6 x + cos“ x sin“ x + sin* x] dx

A: Given that: (tan8xsec6x + cos6xsin4x+sin4x) we solve this integration by using general formulas of…

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

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