Prove each identity  cos t / 1- sin t = 1+ sin t  / cos t

Q: Establish each identity given in attachment.

A: To establish the identity  cosθ+1cosθ-1=1+secθ1-secθ

Q: 11. Verify each identity. sin 2x - 2 a) cot x+ tan(-x) sin(-x)cos x

A:

Q: Prove the identity. Cos(x− 90°) − Cos( x + 90°) = 2 sin x

A: We will use the formulas: cos(A-B)=cosAcosB+sinAsinBcos(A+B)=cosAcosB-sinAsinB

Q: Establish each identity given in attachment.

A:

Q: Prove each identity.   sin  (pi/6 + x) + sin  (pi/ 6 - x) = cos x

A: Given: prove that sinπ6+x+sinπ6-x=cosx we know that sinC+sinD=2sinC+D2cosC-D2

Q: Establish each identity given in attachment.

A: Trigonometric identities help to establish attachment. Since the right-side expression of the given…

Q: Prove the identity. sin^2(θ)−tan(θ)cos^2(θ)−cot(θ)=tan^2(θ)

A: We have to prove the identity                                         sin2θ-tanθcos2θ-cotθ=tan2θ

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

A:

Q: Establish each identity. as attached.

A: We have to establish the given identity: sin 3θsin θ-cos 3θcos θ=2 We know the identity, sin 3θ=3…

Q: Prove each identity    cos 4 A- sin 4 A = cos 2A

A: Given: prove that cos4A-sin4A=cos2A we know that cos2θ-sin2θ=cos2θcos2θ+sin2θ=1

Q: Prove the following identities 1-cos(2x) sin(2x) tan(x)

A:

Q: Prove each identity a. b. 2 tan x 1 + tan² x 1 - sin² x cot² x = sin 2x 1 - cos²x

A:

Q: Prove each identity.   cos  (pi/3 + x) + sin  (pi/ 6 - x) = cos x

A: The given equation is not an identity. The correct identity is, cosπ3+x+sinπ6+x=cosx We will prove…

Q: Establish each identity given in attachment.

A: Given: The identity cos3π2+θ=sinθ The given identity  can be proved as,…

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: prove the identity tanθ =1-cos2θ / sin 2θ

A:

Q: 2-5. Prove each given identity. 2. sinx secx cotx = 1

A:

Q: Establish each identity given in attachment.

A: Establish each identity given in attachment.

Q: Prove each identity. cos x 1- 1+ sinx 0. sinx %3D

A:

Q: Prove each identity.       1/ 1+ cos  t  + 1/ 1-cos t =  2 cosec 2   t

A: We have to prove the identity: 11+cos t+11-cos t=2 cosec2 t Taking LHS part, LHS=11+cos t+11-cos…

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: Establish each identity given in attachment.

A: Given  The identity is sec θ1+sec θ=1-cosθsin2θ .

Q: Prove each identity.   sin (A-B)/ cos A cos B  = tan A  - tan B

A: Consider, sinA-BcosA cosB=sinA cosB-cosA sinBcosA cosB  ∵sinx-y=sinx cosy-cosx siny=sinA cosBcosA…

Q: 11. Prove each identity. T cos 2x + 1 a) cot x %3D sin 2x sin 2x b) 1 - cos 2x cot x c) (sin x + cos…

A:

Q: Prove each identity    cos x - tan x  = cos  2x / sin x cos x

A: We have to prove the identity: cot x-tan x=cos 2xsin x cos x We know that cot x=cos xsin xtan x=sin…

Q: Verify the identity. cos (x+ n) = - c COSX

A: It can be varified using the formula for cos(A+B)

Q: prove the identity.  1+Cos θ= Sin2θ/ 1-Cosθ

A: Given : 1 + cosθ = sin2θ1 - cosθ

Q: Verify each identity. tan 0- 1 2) cos (0 + T) =-cos 0 1) tan 0 1 + tan 0

A: To verify the identities :  1) tan θ - π4 = tan θ - 11 + tan θ 2) cos θ + π = - cos θ

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

A:

Q: Prove each identity.   sec  (A+B)  = cos  (A-B) / cos 2 A - sin 2 B

A: To prove: secA+B=cosA-Bcos2A-sin2B

Q: Prove each identity: = 2 sec2 x 1 A. 1-sin x 1 + 1+sin x

A: Simplify the left hand side of the identity.

Q: Prove the following identities. cos( - ) sin x/2 sin x sec x/2

A:

Q: 4) 3 sin' x + 4cos x- 3+ cos x

A: Our Aim is to verify the identity given below:-3 sin2 (x)+4 cos2 (x)=3+cos2 (x)-(i)

Q: Prove that the following identity is true.   sin4 t - cos4 t / sin2 t cos2 t = sec2 t - csc2 t

A: Given that sin4t-cos4tsin2tcos2t=sec2t-cosec2t

Q: Verify (prove) the following identity. 1-cos(2a) sin(2a) tan x

A: Given,           tanx=1-cos2xsin2xWe know that,          cos2x=1-2sin2x          sin2x=2sinxcosx

Q: Prove each of the following identities.     2 cosec 2 x=  tan x + cot x

A: Given that 2 cosec 2x=tanx+cotx. Start with left hand side as follows.

Q: Prove each identity    1/1 sin t + 1 / 1+ sin  t = 2 sec 2 t

A: To prove the identity: 11-sint+11+sint=2sec2t. Proof: Simplifying the left hand side.…

Q: Verify each identity.  2cot x = sin 3 x + sin x / cos 3 x - cos x

A: We have to verify the identity: 2 cot x=sin 3x+sin xcos 3x-cos x We know the formula for multiple…

Q: Prove each of the following identities.  (sin x 2 cos x)2 =1 - sin 2x

A: To prove:           (sin x  - cos x)2 = 1 - sin 2x

Q: Prove each identity    cot A  = sin 2 A / 1- cos 2A

A: Given cot A  = sin 2 A / 1- cos 2A   We have to prove this identity

Q: Prove each identity.      sin2 x   / (1- cos x )2 = 1+ cos x / 1-cos x

A: To Prove:  sin2x1-cosx2=1+cosx1-cosx

Q: Verify that the equation is an identity. 2 cos x 1. cos X 1. 1+cos x 2.

A: It is trigonometric verification.

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.