5) Prove the law of cosine C=B+ A- 2|A||B| cos 0.

Q: Express in the form a + bi where a and b are real numbers.

A: Here given equation is cos 2π/3 + i sin 2π/3 = cos 60° + i sin 60° = 1/2 + i 3/2

Q: Express in the form a + bi where a and b are real numbers.

A:

Q: 2 v sec 2 1+ cos 0°

A: We have to find the identity

Q: 5) cos A 30 B 16 34 7) sin Z 32 40 24 x, 9) cos Z 24 30 x,

A:

Q: - 1, z = cos-

A:

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

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

Q: Find all general radian solutions: cos x+2sin.xcos.x=0

A: cosx + 2 sinx cosx = 0 cosx ( 1 + 2 sinx ) = 0 cosx = 0.          OR.     1 + 2sinx = 0 cosx =0.…

Q: b) cos(-z)=?

A: In the question we have to find the angle of cosine which is lying in third quadrant as cosine is…

Q: - cos 22.5°

A: Given: a) cos 22.5° b) tan9π8 To find: The exact value.

Q: Cos 30 5-u cosØ do = Tz

A: ∫02πcos3θ5-4cosθdθ

Q: x+(1/x)=2 cos theta , then show that x2+(1/x2 )=2 cos2 theta

A:

Q: B)Convert r = √2 cos (0-) to cartesian.

A: we need to convert polar coordinate into cartesian.

Q: A = %3D (b) If cos (2a) – sin (2æ) = cos( %3D B =

A:

Q: Prove the identity cos(x+y)cos y +sin(x+ y)siny =cos x

A: We have to prove the identity                              cosx+ycosy+sinx+ysiny=cosx

Q: Find the points of intersection between r2 =2 cos20 and r=- %3D 1- cose

A: Find the points of intersection between r2=2cos2θ and r=21-cosθ. for the intersection points both…

Q: */2 Cos Jo

A:

Q: prove the identity  sin^4(t) - cos^4(t) = 2sin^2(t) - 1

A: We know that ,  sin 2 ( t ) + cos 2 ( t ) = 1  cos2 ( t ) = 1 - sin 2 ( t )

Q: 2. COS 12, 2/2

A: We hev to use properties of trigonometric functions.

Q: B)Convert r = √2 cos(0-) to cartesian.

A:

Q: 5. cos A =- and sin B =, both A and B in QIl. 6. cos A = - and cos B = - 2, with A and B in QIII. 17

A:

Q: 1. The formula sinusinv 5(cos (u - v) - cos (u + v)] converts a product of sines to a of

A: sinusinv=12cosu-v-cosu+v

Q: 3. Derive and prove that cos 2x= 2cos'x-1, if the identity cos(A+ B) is given.

A:

Q: Hence prove that sin?a + cos²ɑ = 1 3.2

A: Since you have posted more than one question, we solve the first one for you. For the other…

Q: 3. In (cos)

A:

Q: 6. Prove that: ah cos (i) A sin (ar + b) = 2 sin (ah sin a (ii) A cos (ar + b) = - 2 sin

A:

Q: Verify the identity: (cos2 t + 4 cos t + 4)/(cos t + 2) = (2 sec t + 1)/sec t

A: The given identity cos2t+4cost+4cost+2=2sect+1sect

Q: Homework: de 1-cos 0 1. S-

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the point of intersection of cos(x)=cos^-1(x)

A: We will find the point of intersection using the graph.

Q: Find the points of intersection of r = 1 andr = 1+2 cos 0.

A: General solution of cosθ = cosα is                           θ = 2nπ ±α

Q: 17. cos 2x + 3sin2x = 4 - 3sin?x %3D

A:

Q: 5) Prove the law of cosine C= B+A- 2|Ã||B|co cos 0.

A:

Q: Prove that i2-i0 e-e %3D sincd

A: We have to prove eiθ-e-iθsin θ=2i Now, sin x can be expressed in exponential form as sin…

Q: cos(Inɔx),>o

A:

Q: Prove that sin? 0 – sin* 0 = cos? 0 – cos* 0. cos“ 0.

A: We can use the trigonometric identity, sin2θ+cos2θ=1 sin2θ=1-cos2θ.

Q: 3π b) sin 20 + cosθ = 0,0€ [0, ). 2

A: We have to find the value of they ha in given region

Q: 4. Prove that equations are identities. l– cos4x a) tan 2x =, 1+ cos 4x

A: Given:

Q: Verify the identity. 1 - cos e 4)- 1 + cos e COS sec 0-1 sec e +1

A: From the given problem:   1-cosθ1+cosθ=secθ-1secθ+1   L.H.S.=1-cosθ1+cosθ   As we know that:…

Q: r=1+Cos ở %3D r = 1- sin 0 2. 0.

A:

Q: Prove the identity. TT COS +0+ -sin 0

A:

Q: (a-B) (at sin (a+B) 2- show that cosa – cosß = -2sin 2.

A:

Q: Find the points of intersection between r 2 = 2 cos20 and r =- %3D 1- cose

A: We have to find the intersection between r2=2cos2θ and r=21-cosθ.

Q: sin 0(3sin? 0+ 4cos? 0) = 3 cos 0 + cos³ 0 4. Prove that tan 0

A:

Q: 12 (b) sec ( sin 13

A: Evaluate the form.

Q: Prove that there exists a value of r so that COS I -1 COS %3D

A: Givencosx=cos-1x

Q: 2 Find the points of intersection between r=2 cos20 and r = 1- cose

A: given r2=2 cos 2θ and r=21-cosθwe need to find the intersection between two polar curves

Q: Find point of intersection of the graph r = 1 + cosθ and r = 1 - cosθ

A:

Q: Find all general radian solutions: cos x+2sin xcos x=0

A: According to question, Given trigonometric equation, cos x + 2 sin x  cos x = 0

Q: Prove Sin (A+B)+Sin (A-B)=2SinA.CosB

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.