Prove the following identities: 1. tanx−sinxcosx/(1+cosx) =tanx−sinx

Q: 4. Establish the identity: sec ar - secr sin2 = cos LIC HS O6Y

A: Establish the identity

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: 18. Use periodicity to express sec in p given that sin

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Q: Express tan a using x. 3

A: We have the right-angled triangle. Let us label the small triangle ABC, the big triangle ABD and the…

Q: 3. Express 1+cos2x in terms of cos x. hence a. Evaluate (1 + cosx)dx b. Express 1- cos2x in terms of…

A:

Q: 1- Determine. 4. Cos 'x sinX dx

A: Given:                     ∫cos4(x) sin(x) dx     Solution:                    Integrating the given…

Q: 1 Differentiate y = tan 8x + cos ,x

A: Using differentiation rule,

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

A:

Q: (2) Find the exact value of the following: (i) cos-(-) (ii) tan-V3 (ii) 2tan-1+ tan-1, (iv) sec…

A: (i) cos-1(-1/2) = 2π/3 (ii)tan-1(√3) = π/3

Q: cos 2x +1 Prove that sin 2x

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Q: Prove the trigonometric identity  1+sec2x /over/ 1+tan2x=1+cos2x

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Q: 8-Prove the following identities. ( [Tan2x/ (secx -1)] -1= secx Cos x+[sin2x/(1+cosx)] = 1

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Q: If tan then 1– 2 1+ z2 COS X 8 |N

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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. cos (x-y) 1+ tanx tany cosx cosy

A: cos(A-B) = cos(A) Cos(B) +sin(A) sin(B)

Q: Prove using the IVT. tan-1x = cos-1x has a solution.

A: Given :                      tan-1 x = cos-1 xSolve :                     tan-1 x = cos-1 x…

Q: 3. Prove the identities following identities. 2tanx sin2x %3D 1+tan²x

A:

Q: 3. Express 1++cos2x in terms of cos x. hence a. Evaluate (1+ cosx)dx b. Express 1- cos2x in terms of…

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Q: find the value of so that ky"=-1 at y=. 6. For cos x- sin y=-

A: On solving this by doing differentiation implicitly we get

Q: To evaluate sin*2x cos 2x dx , the identities to be used is/are: 1+ cos4x A sin4x & 2 2 B cos²2x= 1-…

A:

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

A: Given :            tan θ . cos θ = sin θ for any θ ≠ (2k + 1)π2.  To state true or fase.

Q: 2. * 1 Add File 3. * 1 y = tan x + =tan³x 3 4. * y = = cos x 1 Add File y 1 cos³x 3 1 cosx

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Q: Find sin 2x, cos 2x, and tan 2x if tanx = - and x terminates in quadrant II. sin 2x cos 2x %3D tan…

A: Given data,  tan(x)= -(2/3) Where x in 2nd quadrant. A)sin(2x)=? We know that;…

Q: . Suppose csc(A)· where A terminates in QIV, and sec(B) = -3 where B terminates in QII %3D a) First…

A: Note the trigonometric identities :

Q: 3. Prove the identity : sin(x- y) tanx - tany cosxcosy

A: The given identity is, tanx-tany=sinx-ycosxcosy The identity will be true if the left-hand term will…

Q: find solution set of tan-1x-cot-1x=cos-1(2-x)

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Q: Let tan A = 12/5 with A in Q1. Find exact value for cos(2A)

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Q: Q1// prove one only: tan²x-1 tan²x+1 = 1-2cos²x

A: Topic = Trigonometry

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

A:

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. 3T 2 sin(2x) sin(x) = = cos(2x) =…

A: We have to solve above question and find sin cos and tan value

Q: Give the exact value of COS (-) + sin ( 3 V3 O1 2 2 O V2 O 1+v3

A: We need to find the exact value of the given trigonometric ratios.

Q: Suppose that sin 0 = V10 and 90° < 0 < 180°. Find the exact values of sin and tan- JT sin 2 %3D…

A:

Q: ( tan( tan3x)dx Evaluate: cos²3x A -In |sec(tan3x)| + C 3 |cos(tan3x)|+C B © --n |sin(tan3x)|+c O…

A: Evaluate: I=∫tantan 3xcos2 3xdx

Q: Prove the below cos' x sin 3x + sin' x cos 3x 3 sin 4x 4 II

A: Simplification of trigonometry function

Q: ind sin2x, cos 2x, and tan 2.x if tanx = -2 and x terminates in guadrant II. %3D sin 2x ? cos 2x tan…

A: In second quadrant sin is positive and cos &amp; tan are negative.

Q: 1 what are possible values of cos x and tanx? 2 If sinx= Select one: V3 and tanx= 2 1 a. cosx= V3 V3…

A: Consider the right triangle with one angle x degree. Let a be the length of the adjacent side and b…

Q: Verify the following identities. SHOW EVERY STEP!!! a. sin θ/1+sin θ = tan θ secθ - tan2 θ b. 2…

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Q: 4) Verify. cos²(x)[1 C. – tan²(x)] = cos(2x)

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Q: Evaluate: | sech[In cosx]tanx dx A -2 tan -1(e cosx) +C В -2 tan -1(cosx) +C 2 tan -(ecosx) + C (D 2…

A:

Q: (3) (a) Express cos(3r) in terms of sinx and cosr. (b) Prove that -cosz 1+cosI tan %3D (c) Sketch…

A: (3)  (a)  express cos(3x) in terms of cosx and sin x.       (b)  prove that 1-cos x1+cos x=tan2 x2…

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

A: To Prove:

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

A:

Q: Prove that cos(sin-x) = /I– x².

A: Given: sin-1x=cos-11-x2

Q: tan( tan3x) dx Evaluate: cos²3x A - In|sec ( tan3x)|+C 3 B -In|cos( tan3x)|+C В 3 © In|cos(…

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Q: Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = - cos(x) > 0 3 sin(2x) =D…

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Q: The simplest form of tan2x is secx-1 Select one: a. tan x b. cos x +1 C. sec x + 1

A: Given:     To determine: The simplest form

Q: 2x,given  tanx=2 and cosx>0

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…