Lan: prove (:) - - 4. sin x tan =1- cos x

Q: If f(x)= 2ax tanx + b In(cosx) and f'(x)=5 tanx +4xsec?x, then the values of the constants a and b…

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Q: tan? x sec² x + secx Prove -cos x

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Q: 2: Prove that a) cosx tan3x = sinx tan’x b) (sin x + cos x)² = 1 + sin 2x

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Q: Prove the identity : Sino-tane. cos'e Case-1+Sin?0

A: Solution of the problem as follows

Q: I--I---A sin dydx sin:

A: Given I=∫x=12∫y=xxsinπx2ydydx+∫x=24∫y=x2sinπx2ydydx In the given function variable y is in…

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: (a) Buktikan, Prove that, (sin x + cos x)* = sin" 2x + 2 sin 2x + 1. %3D

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: prove that 2. = - Cotx + C 2 |- Cos?x + Sinx

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Q: lim, 0 tan² (7x) cot(11x) (r+7)sinx

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Q: he interval [0,2r) cos (x) sin (x) = 2 cos (x)

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Q: a) Buktikan, Prove that, (sin x + cosx)* = sin 2x + 2 sin 2x +1.

A: The given equation,sinx+cosx4=sin22x+2 sin2x+1

Q: Let cos x = 1/3+z and cos x lies below then x-axis. Find sin(2x), cos(2x) and tan(2x).

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Q: 1) Prove that sin 0 tan 0 + cos 0 = sec 0.

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Q: if Sec X = 2 then tanx +Cos X =

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Q: cos(-x)+sin(x=x) Q4 prove that sinx 2

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Q: coS X sccr+ tan x 1- sinx

A: given,        cosx1-sinx=secx+tanx

Q: 5. If coshx = csc20, prove that 0 = n+ cothe¬x. [Hint: use identity sin(2a + 2n)]

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

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Q: Show that (tan−1 x)'= cos2(tan−1 x) and then use Figure to prove that (tan−1 x)' = (x2 + 1) −1.

A: The objective is to show that:  tan-1x'=cos2tan-1x.   Use the formula: ddxf-1x=1f'f-1x. Here,…

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

A: In question We have given two identities and we'll prove it, (i). Cos(π + x) = - Cosx  (ii). Cosx…

Q: Let S(x) 9 sin x + 9 cos x "(x) 3= r(-)-

A: A function is given as fx=9sinx+9cosx. The objective is to find the first derivative f'x of the…

Q: If 1, = | x" sin x dx, prove that 1, = nx"-! evaluate -1,. sin x- x" cosx– n(n-1)I, 2. Hence, = NX…

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Q: TT True or False tan 0 • cos 0 sin 0 for any 0 # (2k + 1) %3D

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

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Q: Prove 3n - T, 2 sin? x – sinx cosx – 2 cos? x=0 in has five root's Hint. Intermediate value theorem

A: Corollary of Intermediate value theorem :- If a continuous function has values of opposite sign…

Q: 2) Verify. cot8 ese 6 %3D sin 6 tan 6

A: Use the following identities:

Q: If () Z = tan || then 2z sin x 1+ z2

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Q: Prove ONE of the follow sin x+ cos 2x-1 tan x %3D a) cos x-sin 2x

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Q: 8. Prove that tan? 0 + cos? 0 + sin² 0 = sec² 0. %3D

A: Explanation and solutions is given below....

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

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Q: the exprression csc x/sec x  is equivalent to: 1.  sin x 2. cos x 3. tan x 4. cot x

A: *to find:-  csc x/sec x = ?

Q: what is the value of x if 2tan x / (1-tan^2x) = cot56

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Q: ≤ Lºin( Verify that f(x) = sin() is an odd function and use that fact to show that 0 < sin(√√x) dx ≤…

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Q: (b) Can we use the IVT to conclude that f (x) = tan(x) equals 0 for some c in (0, 1)? %3D

A: We can answer first question among which you asked as per the honor policy. please resubmit the…

Q: Q4) Prove that 1- Cos +x) = sin x, 2- (sin x +cos x) sec x see' x

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Q: Prove (cosa + cosB) + (sina + sinß)° = 4cos²- « - B) %3D

A: Prove this equation by using some trigonometry identity

Q: Prove (Start either from the LHS or the RHS but DO NOT work from both sides at the same tim 3. Prove…

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Q: TO For x such that 0 < x<, the expression 2. V1-cosx V1- sin'x COS"X is equivalent to: sin x COS X

A: I am solving this in step 2

Q: prove that cos^2 x/2= tanx+sinx/ 2tan x

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Q: Prove the identity. secx (1-sin'x) = cannot b cosx %3D

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Q: tx)+ Sin(꼴-)- -26S X %3D Prove sin

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Q: 1. Which expression is equal to sec x tan z sin x using identities?

A: We can use simple trigonometric identities to solve the given equation.

Q: Prove using trig identities sin 20° =1 V3 cos 20° – 2 sin 40°

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

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

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

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