Prove: sin x tan x+cos xcot x+2 sin x cos x = tan x+ cot x + cos²

Q: (A) Verify the identity (i) (1 + tan² x)(1 - sin2x) = 1 sec x - 1 %3D tan x (ii) tan x sec x + 1 1+…

A: We have to prove the identities.

Q: 2: Prove that a) cosx tan3x = sinx tan’x b) (sin x + cos x)² = 1 + sin 2x

A:

Q: 5- Prove that a) tan x (csc x – sin x) = cos x b) 1+ sec?x sin?x = sec?x

A:

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

A:

Q: Expand and simplify: sin(x+3)-cos(+ x) 6 COS X

A:

Q: Prove that: 1) csc 0 + tan 0 . sec 0 csc 0.sce20 1-cos" x 2) sin x .cos x tan x 3) 3 cos' x-sia x+1…

A:

Q: Lan: prove (:) - - 4. sin x tan =1- cos x

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Q: Prove the identity. csc (-x)- sin (-x)=- cos x cot x

A: we know that sin(-x)=-sinx than csc(-x)=1/sin(-x)=1/-sinx than  1/-sinx -(-sinx) (1/-sinx)+sinx…

Q: Prove the identity. cosx 1- sin x 1 = tan x cos x

A: We need to prove the following identity cosx1-sinx - 1cosx = tanx

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

A:

Q: Prove the identity. tan(x -)- -cot(x) TC tan x 2 %3D sin(x - ) | tar(x-)- sin(x) cos) - cos(x) sin…

A:

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

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

Q: Prove the identity. sin(2x) 1+ cos(2x) tan(x) = 2 sin(x) · sin(2x) 1+ cos(2x) 1+ (2 cos?(x) – 1) 2…

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Q: Verify the identity. sin x = csc x + cot x 1-cos x

A: This question can be solved by appropriately arranging the given options in the blanks.

Q: 1 Verify the identity 1 = 2 tan x sec x %3D 1-sin x 1+sin x

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Q: 7) Verify the identity (cot x – csc x)(cos x + 1) = -sin x

A:

Q: Verify the identity.   1 + sin x 1 − sin x  −  1 − sin x 1 + sin x  = 4 sec x tan x

A: The given identity is,

Q: Prove the identity: 1 sin x COS X sin x + cos x (sin x + cos x)2 1+2 sin x cos x

A: Given- 1sinx+cosx-sinx(sinx+cosx)2=cosx1+2sinxcosx Here we will use the following formula-…

Q: Verify the identity. tan(0) sin(0) + cos(8) = sec(0) tan(0) sin(0) + cos(0) : sin(0) + cos(0) cos(0)…

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

A:

Q: Verify. the. identity cos(x)sin(x)tan(x)=csc(x)-cot(x)-cos^2(x)

A: To verify: cos(x).sin(x).tan(x)=cosec(x)-cot(x)-cos2(x)

Q: Evaluate: / [cos(x) – sin(x«) ]dr A cos(x) + sin(x) +C - cos(x) + sin(x) +C

A: In this question we will use basic of calculus i.e concept of integration. We will simply use the…

Q: 1 Prove that sin x tan x = cos x. cosx

A:

Q: Verify the identity tan(x) Cos(x) csc(x) (1 sec(x)) 1 1cos(x) 1cos(x) tan(x) cos(x) tan(x) 1 -…

A: Given identity to be verified is

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: Prove the following identities 1. (cot x − csc x)(cos x + 1) = − sin x 2. sin 3x + sin 7x/cos 3x −…

A: 1. (cot(x) - cosec(x))(cos(x) + 1) = -sin(x)   Taking LHS, = (cot(x) - cosec(x))(cos(x) + 1) =…

Q: x=cos¬! 1 prove that sec" X= cos

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

Q: * tan°(x) cos“(x) 1 tan7(x) 1 tan (x) O tan7(x),

A:

Q: Verify the identity 1- sin x (sec x- tan x)2 = %3D 1+sin x

A: secx-tanx2=1cosx-sinxcosx2=1-sinxcosx2=1-sinx2cos2x=1-sinx21-sin2x…

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

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Q: rove the identity. sin(3x)/sin(x)cos(x)=4cos(x)-sec(x)

A:

Q: Prove tan x + cos x = sin x (sec x + cot x).

A: We have to prove the identity: tan x+cos x=sin x sec x+cot x We know the relation between…

Q: Verify the identity (1+sin x)(1-sin x)=cos2x   (sin x + cos x)2 + (sin x - cos x)2=2   cot(x) =…

A: (1+sin x)(1-sin x)=cos2x Apply FOIL method to expand left side

Q: Prove the identity. sin2(x)−tan(x)/cos2(x)−cot(x)=tan2(x)

A:

Q: Verify the identity. sin³(x) + cos³(x) = 1 – sin(x) cos(x) sin(x) + cos(x) sin3(x) + cos³(x) sin(x)…

A: we know that  a3+b3=a+ba2-ab+b2

Q: Prove the identity. sin(n-x)сos(n+x)tan(2π − x) T 3π 3π sec+ x)csc(³7-x)cot (³7 + x) = sin^x - sin²x

A: I have appended the formula used in the solution part of the question

Q: sin 2x sin x Cos 2x %3D Prove that 4 cos x - sec x Cos a

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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

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Q: Simplify. 1+ sin 2x + cos 2x cos X O 2 cot x O 2 tan x 2(sin x + co x) 2(sin x - cos x)

A: Given: 1+sin2x+cos2xcosx

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: Q3:A| Prove that:- cos x 1) 1+sin x 1+sin x = 2 sec x cos x tan? x 2) tan? x+1 = sin x

A: topic - trigonometric identities

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: 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: Prove sin 2  x/2=  tan x - sin x / 2 tan  x

A: The given identity is sin2x2=tanx-sinx2tanx

Q: Prove the identity. tan(x - ) - sin(x -) -cot(x) %3D tan(x -) - sin(x) cos - cos(x) sin() + sin(x)…

A: We have to solve

Q: Verify the identity. 1+ sin(x) = (tan(x) + sec(x))² 1+ sin(x) 1 - sin(x) 1- sin(x) 1+ sin(x). 1 +…

A:

Q: Prove the identity. 4(tan(x) – cot(x)) tan2(x) – cot2(x) | = 2 sin(2x) %3D

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.