Prove that the following identity is true. tan (A + B) = (tan A + tan B)/(1 − tan A tan B)

Q: Please solve a question on hyperbolic functions.

A: Let us first find x + iy and its complex conjugate x – iy. Complex conjugate can be found by…

Q: Find the exact value of tan (a + B) under the given conditions. 24 cos B = tan a== 21 25 2 B<T

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Q: Prove the following identities and give the valuesof x for which they are true

A: Let tan-1 (x)=α⇒x= tan αHence, we have tan 2α=2 tan α1-tan2 α

Q: tan'z- sin a = tan a - sin"

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Q: If A +B = 90° Prove that tan A tan B+ tan A cot B sin' B = tan A sin A sec B cos A

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Q: 1. Given that sin a =- and sin B -find tan (a + B) if both a and B are in QIV.

A: As per guidelines, I can only solve first question remaining can be reposted.

Q: Prove that: (1 – sin? x)(1 + tan? x) = 1

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Q: (a) Prove that, if n> 1 is a natural number. then tan"-(r) /- tan" (r) dr. tan" (r) dr n- 1 Use this…

A: Prove that ∫tannxdx=tann−1xn−1−∫tann−2xdx

Q: 10) Find the exact value of: tan +tan B tan (A+B)= -tan A tan B tan + tan 1-tan tan 5T TC 4 12 5TT…

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Q: 1 Show that (tan-' x) : 1+x?

A: We use Trigonometry identities and inverse Trigonometry to solve this proof

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

A: To prove: 1-cos xsin x=sin x1 + cos x Use the trigonometric identity, sin2x + cos2x = 1

Q: PROVE that sin x = V1 – cos² x is NOT an identity. -

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Q: Find the exact value of cos(2 tan−¹(-5₂2)). 12

A: Given cos2tan-1512

Q: - Prove the following identities: Sin( A+B)+ Sin(A-B)= 2.SinA.CosB Sin( A+B) a) b) tan A+ tan B =…

A: Given: sin (A+B)+sin(A-B)=2 sin A cos B tan A+ tan B =sin(A+B)cos A. cos B…

Q: Prove that the following identity is true. sec ? + 1 / tan ? = tan ? / sec ? − 1

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Q: Prove the following identity: tan? x +1 = sec² x

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Q: Considering only the values of a and Bf sec asec Bcos (a + B) is defined, sec asec Bcos (a + B)…

A: Given that trigonometric equation simplifying below;

Q: Use the following information to determine cos(2x). tan(x) = -4 and cos(x) is positive %3D Answer…

A: 1+tan2x=sec2x cos(2x) = 2cos2x-1

Q: Prove that each of the following identities is true.   sec x +tan  x  = 1 / sec x  - tan x

A: We know that identity, sec2θ-tan2θ=1              ⋯⋯1 And a2-b2=a+ba-b            ⋯⋯2

Q: Prove: 1. tan (A/2) = - cos A 1 + cos A sin A 1+ cos A 2. tan (A/2) = ±

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Q: Establish the identity: tan(0 + ™) tan 0 TT

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Q: Verify the following identities: 1. cot(x) + tan(x) = sec (x) · csc (x) CO %3D

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Q: Prove the following identity: sin(2a)/cos(2a)−1=1/−tan(a) sin(2a)/cos(2a)−1=

A: We use the double angle identities in both numerator and denominator.

Q: (a) Prove that, if n > 1 is a natural number, then tan"-(r) tan"-2(r) dr. n-: tan" (r) dr n - 1 Use…

A: The solution is given below :

Q: Prove the following identities and show complete solution 1– tan x = (2 tan x – sec?x)(tan x – 1)

A: To prove: The identity 1-tan3x=2 tanx-sec2xtanx-1 Formula used: Algebraic identity:…

Q: Show all work to find the exact value of tan(a - 8) given the following conditions: 0 <a<: cos ß =…

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Q: If A +B = 90° %3D Prove that tan A tan B+tan A cot B sin? B = tan A sin A sec B cos A

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Q: (a) Prove that, ifn>1 is a natural number, then tan"(r) dr tan-(r) tan" (4) dr. R-1 Use this formula…

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Q: Which of the following give the value of tan z? tanh(-iz) 2iz +1 2. e2iz-1 e2iz 1 2iz +1 tanh(-iz)…

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

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Q: Prove the following identities: 1 1 a) tan x+ tan x sin xcosx

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Q: Prove that there exists a value of a so that COS I COS

A: The given equation is: cosx=cos-1x To prove that there exists a value of x.

Q: Prove that c) 1-tan?A -Cos 2A Htan?A

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Q: m -1 :If tan A = n tan B and sin A = m sin B, prove that cos A = n -1

A: Given that  tan A=n tan B sin Acos A=nsin Bcos B ................equation 1 also given that  sin A=m…

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

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Q: Show that the following holds true. 1 csc A = sec A = cot A = sin A cos A tan A sin A = cos A tan A…

A: In any right angled triangle, sin A=OppositeHypotenusecos A=AdjacentHypotenusetan…

Q: Verify the identity cos(a+b)/cos a cos b = 1 - tan a tan b

A: Verify the identity cos(a+b)/cos a cos b = 1 - tan a tan b

Q: prove the following identity (1-tan2(x))/(1+tan2(x))=2cos2(x)-1

A: To prove

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

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Q: Evaluate: / tan( tan3x)dr cos?3x i -In |sec(tan3x)|+C A 3 В - In |cos(tan3x)|+C -In |sin(tan3x)|+C 3…

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Q: prove the identity cos(a + b)/cos(a) cos(b)= 1 − tan(a) tan(b)

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Q: Find the exact value of tan (a+ B) under the given conditions. 13.0<a< cos B = p 0<p< 21 0<B<3 sin a…

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Q: If A +B = 90° %3D Prove that tan A tan B + tan A cot B sin' B = tan A sin A sec B cos A

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

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Q: Verify (cos(a+b))/ (cos a cos b)=1-tan a tan b.

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Q: Prove that the following identity is true: tan(A+b)=(tanA + tanb)/(1-tan A tan b)

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Q: Prove that the following identity is true. sec 0 + 1 tan 0 %3D tan 0 sec 0 – 1

A: Given, secθ + 1 tanθ  Multiplying the numerator and denominator with secθ -1secθ -1 secθ + 1 tanθ *…

Q: Find cos a if tan a= (√2)/2 and sin a=-(√3)/3

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Q: Prove the following identities: sec(0) + tan(0) (a) cot(0) + cos(0) cos?(x) tan(0) sec(0)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: What is the smallest number x such that tan e^= 0.

A: Given: The equation tanex=0 To find: The smallest number xsuch that the given equation is satisfied.