Evaluate composite functions with inverse trigonometric functions in the form f(f-1(x)) or f(g-1(x)) Question 197 If n = E D radians, simplify the expression tan¬' (tan n). If the answer is undefined, enter Ø.

Q: Is sin-1 x the same thing as1/sin x?

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Q: Verify the identity:csc x - cos x cot x = sin x.

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Q: cosx+sinx=cos(2x)  Prove that tanx=-1

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Q: * If f(x) = (sin-'(4x + 7))', then f'(x) = Note: The inverse of sin(x) can be entered as arcsin(x)…

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Q: EXAMPLE 5 Evaluating Trigonometric Functions 4 -- and cos 0 > 0, find cos 0 and tan 0. Given sin 0

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Q: Evaluate the definite integral of the trigonometric function. Use a graphing utility to verify your…

A: To integrate

Q: Find the exact value sin[sin^-1(-4/5)-tan^-1(3/4)]

A: Use relation between sin-1 and tan-1   The expression is re written as,

Q: 8. Find the exact value. sin(tan¬1 x)

A: Convert tan-1x into sin-1x then calculate exact value

Q: In(|tan(x) sin(x)]) = 2 In(|sin(x)|) + In(|sec(x)|)

A: i will use the log rule: ln a +ln b=ln(ab) and some trigonometric rules.

Q: Use a trigonometric identity to show that the derivatives of the inverse cotangent and inverse…

A: To show: The derivatives of the inverse cotangent and inverse cosecant differ from the derivatives…

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

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Q: Evaluate the definite integral of the trigonometric function. Use a graphing utility to verify your…

A: Topic- definite integration

Q: tanºx sec*x dx. Use trigonometric groups..

A: Given:        ∫0π4  tan5x sec4x dx

Q: Verify the identity -tan x  = cos 3 x - cos x / sin 3 x + sin x

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Q: verify the trigonometric identity: cot x( sec x-cos x)= sinx

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Q: Establish the identity. (sec 0+ tan 0)( sec 0- tan 0) = 1

A: We have to prove

Q: Determine

A: We will solve for the angles.

Q: Prove the Calculus identity sin-(x) + sin-(/1 – x²) 2 x € [0,1], where sin-, denotes the usual real…

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

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Q: Verify the Trigonometric Identity; show steps. sin (x) – cos²(z) sec2(x) – csc²(x) sin(x) + tan(x)…

A: We need to verify trigonometric identity.

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

A: sinx1+cosx=sinx1+cosx×1-cosx1-cosx=sinx1-cosx1-cos2x     ∵a+ba-b=a2-b2=sinx1-cosxsin2x…

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

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Q: $66)= Sinx+ Cos>x.

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Q: How do you solve this and can you show me step by step?

A: If we dont restrict the domains of trigonometric functions then they are not one-one and so inverse…

Q: Verify identity sec x - sec x sin2 x = cos x.

A: Given ,           sec(x) - sec (x)sin2(x) = cos (x).

Q: Find sin x if sin x – cos x x = 3 sec x

A: Consider the given trigonometric expression, sinx-cosx=13 now square both side of the equation,…

Q: True or False sin( - θ) + sin θ = 0 for any value of θ.

A: To check: Whether sin-θ+sin θ=0 is true or not for any value of θ. Concept used:  Trigonometric…

Q: Give 2 examples on Evaluating Inverse Trig Functions using Sin difference Identities

A: Topic :- trigonometry

Q: Verify. the. identity cos(x)sin(x)tan(x)=csc(x)-cot(x)-cos^2(x)

A: To verify: cos(x).sin(x).tan(x)=cosec(x)-cot(x)-cos2(x)

Q: 15. Verify the identities: a) csc x -sin x = cos x • cotx b) tan²0 1 + sece 1 - cose cose

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Q: Express the value of the trigonometric function tan⁡(π-3i) in terms of x+yi.

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Q: tan x csc x-tan x sin x tan +cos x cos? Prove = COS s“ x csc x Show all work to receive credit

A: We have to prove

Q: Establish the identity. sin 0 1 sin 0- 1 1 csc 0

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Q: Evaluate the definite integral of the trigonometric function. Use a graphing utility to verify your…

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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: cos² (In x) sin²(In x)

A: Given: I=∫cos2(lnx)sin2(lnx)xdx

Q: Find the exact value. -5n sin- 6. Type + or - [ ?

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Q: Prove the identity. csc (-x) – sin (-x) = cosx cotx

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Q: Find the exact value of the expression. Show work.

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Q: Verify the identity: csc x - cos x cot x = sin x.

A: Given identity, cscx-cosxcotx=sinx

Q: Prove the identity. sin2(x)−tan(x)/cos2(x)−cot(x)=tan2(x)

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Q: Verify the identity: cot(-x) sin x = -cos x

A: cot(-x)=-cot(x)cot(x)=cos(x)sin(x)

Q: Summarize how the derivatives of inverse trigonometric functions are related to the derivatives of…

A: dsin-1xdx=11-x2dcos-1xdx=-11-x2dtan-1xdx=11+x2dcot-1xdx=-11+x2dsec-1xdx=1xx2-1dcsc-1xdx=-1xx2-1

Q: Verify the identity : sin(x + π)/cos (x + 3π/2) = tan2 x - sec2 x

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Q: a) Express sin(2 cos¯'x) in an unction and find its domain and range. algebraic form. Furthermore,…

A: Given: sin ( 2 cos-1(x)

Q: Verify the identity: cos x/(1 - sin x) + (1 - sin x)/cos x = 2 sec x

A: The given identity is cosx1-sinx+1-sinxcosx=2secx

Q: sin- (b) sin 3

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

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Q: Verify the identity: (sin x + cos x)/sin x - (cos x - sin x)/cos x = sec x csc x

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