1. tan xsin x + cos x

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

A: To Prove:cosx-ycosxcosy=1+tanxtany

Q: 60. tan(cos−1 x + 12 ) = √4 − (x + 1)2x + 1

A: Given :  tan(cos- x + 1/2) = √4 - (x +1)2 /x + 1 where, cos- (x + 1/2), cos-θ = Base/Hypotenuse,…

Q: Prove the identity. 3 sin(x - y) 3 tan x - 3 tan y = cos y cos x

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Q: Prove that: (1 – sin? x)(1 + tan? x) = 1

A:

Q: 2+tan x cos³ x

A:

Q: 6. Prove the following sin (x + n) = -sin x cos x+ 2 - sin x

A: Part a,Given,           sinx+π=-sinx

Q: Prove the identity. 3. cos X sim x= 2. S1in X-Sin x) COSX

A:

Q: Verify the identity : cos (x - π/4) = √2(cos x + sin x)/2.

A: We use cos(A-B)=cosAcosB+sinAsinB formula

Q: 3. Prove the identity of tan x + cot x = csc x sec x. Work on the left side.

A:

Q: 5. Verify the identity: sin(x- y)cos y+cos(x– y)sin y = sin x

A: Explanation of the solution is given below.....

Q: In Exercises 7–12, one of sin x, cos x, and tan x is given. Find the other two if x lies in the…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: II. Find tan (A +B) and tan (A - B) if: 5. cos A = - and sin B =, both A and B in QII.

A: As per bartleby guidelines we only give first question answers.

Q: Prove the identity 1/Cos X - 1/Sec X = Tan X * Sin X

A:

Q: Prove: 1. tan (A/2) = - cos A 1 + cos A sin A 1+ cos A 2. tan (A/2) = ±

A:

Q: Establish the identity. cos e 1 cos 0- sin 0¯ 1- tan 0

A: Given,            cosθcosθ-sinθ=11-tanθ

Q: Osl 2. 2Sin x- CosX+1 = 3 tan x 2 Cos?x

A:

Q: 1 1. Use basic identities to simplify the expression secx cos x + cos x secx

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Prove that cos 2x | tan x + cos 2x ).

A: we need to prove, 1-Cos2x1+Cos2x = tanx

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 the identity: (sin x – cos x)(sin x + cos x) = 2 sin² x – 1

A: As value of cosθ and sinθ revolves around +1 to -1 , they take different values depending on the…

Q: III. Verify the identity. 5.) 1-Cos 2x tan?x %3D 1+ cos 2x

A:

Q: 31) 2 tan x cos x+2 cosx= tan.x+1

A:

Q: 5л Compute the exact value of tan ( + 4 ). 6.

A:

Q: Prove the identity. cos(x + y) + cos(x – y) = 2 cos(x) cos(y)

A: It is given that,

Q: B) Prove that: cos? 0 – sin? 0 1-tan? 0 =- 1+tan? 0

A: B)cos2θ-sin2θ=1-tan2θ1+tan2θRHS1-tan2θ1+tan2θ

Q: Prove: sin? x 2 cos“ = cos 2-2cos x

A: We will use basic properties of trigonometric ratios

Q: 9. Verify the identity. (1–cos² x)(csc x) cot x 2 sin x(tan x) a)a

A:

Q: Prove the following identity 1+ cos(2x) 1 sin(2x) tan(x) 1+ cos(2x) sin(2æ)

A:

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

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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: 16. Establish the identity: os 0)² + (sin 0- cos 0)2 = 2 %3D

A: We need to establish the identity  (sinθ+cosθ)2+(sinθ-cosθ)2=2

Q: 117 in terms of sin(x) and cos(x). 6 Rewrite cos ( x +

A: We have to solve

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

A:

Q: x=cos¬! 1 prove that sec" X= cos

A: Given sec-1x=cos-11x

Q: - Let cos x 5. Find all possible values of sec x – tan x %3D sin x

A: Given that  cosx=13 To find the possible values of  secx-tanxsinx The identities used here…

Q: Prove identity: 4 sin x cos x (1 – 2 sin? x) = sin(4x)

A:

Q: 24. Prove the identity 1 – (sin x – cos x)2 = sin 2x

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

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Q: Prove cos* x – sin* x =1–2sin² x

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Q: 7. Prove the identity. 1-cos 20 tan 0 %3D sin 20

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Q: Complete the statements.

A: a). As x→-1+, sin-1x→-π2

Q: 7. Verify the identities: tan x tan x tan20 1-cos e a) 1+sec x = 2 csc x b) sec 0+1 %D 1-sec x cos e

A:

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

A: *formula:- cos(A+B) = cosA*cosB - sinA*sinB.

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: 1. Verify the expression cos(x) + sin x tan x = secx.

A: Given, cos x + sin x tan x = sec x

Q: 4. Verify the identity: 1 cos(x)+1 1 + cos(x)-1 -2 csc(x) cot(x)

A:

Q: 37 in terms of sin(x) and cos(x). Rewrite cos 4

A:

Q: what is the deivative oF: tan(3x) eX y = In x

A: The given function is: y=2xtan(3x)ex8ln x

Q: 7. Prove the identity. – sin 3 TT -x= 0 2 sin +x 2

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.