Prove the identities. (a) tan theta  sin theta  + cos theta = sec theta (b) (2 tanx)/(1+tan^2x) = sin2x

Q: sin 2x Verify 1+ cos 2x = tan x.

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Q: (tan® – sin®)²+(1 – cos®)²= (1 – sec0)²

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Q: Verify the identity : 1-cosx sinx = 2 csc x sinx 1– COsx 2.

A: Given- 1-cosxsinx+sinx1-cosx=2cscx To verify- The above identity. Identity Used- sin2x=1-cos2x

Q: cos8x - cos 6x Using Sum to Product identities, verify -tan x sin 8x + sin 6x

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Q: Prove the identity. sinx 1. cotx 1-cosx sinx

A: 1 - sin2x = cos2x

Q: cosx+sinx=cos(2x)  Prove that tanx=-1

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Q: Verify the identity: (cos 3x - cos x)/(sin 3x + sin x) = -tan x.

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Q: If tan x = -1/3, cos x > 0,, then | sin 2x -6 cos 2x -1 tan 2x -3/4

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Q: In(|tan(x) sin(x)]) = 2 In(|sin(x)|) + In(|sec(x)|)

A: i will use the log rule: ln a +ln b=ln(ab) and some trigonometric rules.

Q: 4. 1 + tanx 1- sinx

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Q: Verify identity (csc x - cot x)2 =(1 - cos x)/(1 + cos x).

A: The given identity is csc x-cot x2 =1-cos x1 + cos x

Q: Evaluate sin 2x -dx sin x sin x+- 3 3

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Q: Verify the identity -tan x  = cos 3 x - cos x / sin 3 x + sin x

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Q: Prove the identity. sin x+ 2. = cotx sin (n-x)

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Q: If tan x = 3, cos x > 0, , then - sin 2x cos 2x tan 2x %3D

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Q: Prove the identity. sin'x cos'x = (cosx-cos x) sinx 3. cos x- cos x) sinx

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Q: Prove the identity. cosx/1-sinx - 1/cosx = tanx

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Q: -sin^2(x)=cos(2x) from [-pi, pi]

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Q: Prove cos x (1+sinx 1-sinx sin x. 4 1-sinx sinx+1/

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Q: Verify identity sec x - sec x sin2 x = cos x.

A: Given ,           sec(x) - sec (x)sin2(x) = cos (x).

Q: Verify the identity.

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Q: If cosx = -2/3 and tanx < 0, then sin(x)= tan(x)=

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Q: 1-cosx sinx B: Prove sinx 1+cosx

A: Consider,  LHS=1-cosxsinx       =1-cosxsinx×1+cosx1+cosx       ....(muliply and divide by 1+cosx)…

Q: Prove the identity. sin(-0) sec(-0) cot(-0) = 1

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Q: tanx+secx-1 1+sinx tanx-secxx+1 cosx

A: We have prove trigonometric identities tanx+secx-1tanx-secx+1=1+sinxcosx Left hand side:…

Q: 1-sin' x 3D sin.x 6. cosxcotx

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Q: VERIFY THE IDENTITY

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Q: 2. Verify: sin x+tan x %3D sin2x sec x cscx+cotx

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Q: sin 2x+cos2x+1 1- Prove cot x sin 2x-cos 2x+1

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Q: 1-cos2.x sin 2.x : tanx

A: Given- 1-cos2xsin2x : tanx To Simplify- The above expression. Formula Used- cos2x=1-2sin2x and…

Q: tan x csc x-tan x sin x tan +cos x cos? Prove = COS s“ x csc x Show all work to receive credit

A: We have to prove

Q: csc*x - cot"x = (1 + cos²x)/sin²x

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Q: cos^2x+sin^2x/cos^2x=

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Q: 3 cos xdx 1-sinx

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Q: sin 3x cos“ 3xdx

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Q: Verify the identity : sin(x + π)/cos (x + 3π/2) = tan2 x - sec2 x

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Q: 8. If sin x- cos x = 3, find sin x sec x

A: given: sinx-cosx=13 to find: sinxsecx

Q: 1 + tan x 58. cosx tanx sinx - sin x

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Q: Verify the identity: tan2 2x + sin2 2x + cos2 2x = sec2 2x

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Q: . Evaluate cos 3x sin² 3x dx

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Q: Prove the identity. sec(-x)-sin(-x)tan(-x)=cosx

A: sec(-x)-sin(-x)tan(-x)=sec(x)-(-sin(x))(-tan(x))=sec(x)-sin(x)tan(x)

Q: -CSCX · COSX = -Cotx - 1 cosxsec2x = COSX 1 1 sec2 x+cot2 x csc2 x+tan2 x CScx 1+ cot2 x = sinx

A: NOTE: Refresh your page if you can't see any equations. .

Q: |- Sin X Cot X Cosx SinX -

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Q: Find exact function values for: a. sin(α/2) b. cos(α/2) c. tan (α/2) cosα = 12/13, (3π)/2 < α <…

A: The given trigonometric ratio is cosα=1213 ,where3π2&lt;α&lt;2π (a) To find the value of sinα2…

Q: tan 0+ sece- 1_ 1+ sin0 cos 0 Show that tan0-sec0+1

A: Given the trigonometric equation (identity) is: tanθ+secθ-1tanθ-secθ+1=1+sinθcosθ To show that, the…