Prove: sin? x 2 cos“ = cos 2-2cos x

Q: Cos x = Cos" x 1-

A: In this question we have to prove cosx=cos-1x.

Q: If sino + sin'0 +sin' 0 = 1, then prove that cos 0-4 cos* 0+8cos 0 = 4.

A: sin2 x + cos2 x = 1.

Q: (-n *) Prove sin? x – sinx cosx – 2 cos? x =0 in п, 2 has five root's Hint. Intermediate value…

A:

Q: Prove the identity. cosx sin (x+y) – sinx cos (x+y) = sin y %3D

A:

Q: Prove that: 1-tan? 0 cos? 0 - sin? e %3D 1+tan? 0

A: A function is said to be a rational function if it is given as the ratio of some values.  The…

Q: Establish the identity. 1- cos 0 sin 0 = 2 csc 0 sin 0 1- cos 0

A: We have to prove, 1-cosθsinθ+sinθ1-cosθ=2 cscθ

Q: 3 Prove the identity: sin30 = sin® –sin30 using De Moivre's theorem.

A: To prove the given identity ,we have to use De Moivre's identity.

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+sinZA Cos A-SinA

A: To Prove: cos3A-sin3AcosA-sinA=2+sin2A2

Q: Prove a (cosa + cosß) + (sina + sinß) = 4cos² (@ - B) 2 %3D

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

A:

Q: Prove the identity. cos²x 1+ sinx (1– sinx)? 1- sinx

A:

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

A:

Q: Prove sin?x tan²x – cos?x = sec²x - 2

A: To prove : sin2x tan2x - cos2x = sec2x - 2

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

A:

Q: Prove the identity. sin'x cos'x= (cos'x- cos"x) sin x

A:

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: Prove the identity  Cos x/1+sin x + Cos x/ 1-sinx = 2sec x

A:

Q: Prove the identity. 1- cos X = (csc x- cot x)² %3D 1+ cos X

A: Prove that , 1-cosx1+cosx=cscx-cotx2

Q: 4. Prove the identity csc 0 – sin 0 = cot 0 cos 0.

A:

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

A:

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: Prove the identity. cosx- cos 7x tan 3x %3D sinx+ sin 7x

A: Here we use basic formulas of trigonometric ratios to find addition and subtraction.

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

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

Q: Establish the identity. 2 cos - 0 1- 1+ sin 0 = sin 0

A:

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

A:

Q: Prove the identity. s (xxy) sinx- sin (x-y) cosx= siny cos

A:

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

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: The integartion of [sin(sinØ)]Ø cos dø Is: cos(sin0)+C -sin(cos Ø) + C O -sin(sinØ) + C O -cos(sinØ)…

A:

Q: Prove the identity: sin(0)-co sin (0) +cos (0)–1 cos (8)+1 sin(0)+1 cos(8)

A: On proving this we will get

Q: 1) Prove that cose-sin*e 1- tan?e cose

A: Trigonometric identities help to prove the required expression. The algebraic formula…

Q: Prove that sin? 0 + cosª 0 = sin“ 0 + cos² 0.

A: Using fundamental identity of trigonometry.

Q: VERIFY THE IDENTITIES

A: To verify

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

A:

Q: Simplify sin “ z – cos“ æ O 2cos (x) - 1 O 2sin*(x) - 1 O 1+ 2sin*(x) O 1+ 2cos (x)

A: Using trigonometric identities.

Q: Prove the identity: sin² 0-cos²0 sin 0+ cos 0 = sin 0-cos0 -

A:

Q: Prove the identity. sin x 1+ cos x 1- cos x sin x

A:

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: Prove that cos(sin-x) = /I– x².

A: Given: sin-1x=cos-11-x2

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

A:

Q: 8. Prove the identity sec 0 – cos 0 = sin 0 tan 0

A:

Q: Prove that sin 4A = 4sinA cos³A – 4 cosA sin'A.

A: we have to show that the following

Q: TT CoS-+COs sin 3 = sin Prove that Sin 3 - 6. 6. 2.

A:

Q: Prove that; (a) cos4θ- sin4θ = cos 2θ  (b) Sin (π/4 + A) + Sin (π/4 - A) ≡ √2 cos A

A:

Q: Verify the identity. (1 – cos"(x)(1 + cot*«») = (1 - cos (x)(1 + cot°») - sin°C«) - 1 + sin (x) =…

A: Solved below

Q: Prove the identities: (sec 0 – cos 0)(csc 0 – sin 0) = sin 0 cos 0 -

A: Topic - trigonometry