Using Inverse Functions sec2 x − 2 tan x = 4 Original equation 1 + tan2 x − 2 tan x − 4 = 0 Pythagorean identity tan2 x − 2 tan x − 3 = 0 Combine like terms. (tan x − 3)(tan x + 1) = 0 Factor.

Q: tan 0 + tan? 0 = sec* 0 - sec² 0

A: This question is taken from trigonometry in which we have to prove the given identity  We can write…

Q: cos(- 3. Find the exact value of '12' 4 sin' x 2 sin(2x) = 4. Prove tan x

A: 3 We have to find exact value of cosπ12          since we know that cosπ6=32          since we…

Q: sin x 14) Simplify: sec(x) tan x A) 1 C) sec² x 7n B) tan(x) D) sin(x)

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Q: sin160°- cos 250° sin 330°.cos(-290°) 2 sin? 33°+ sin 123°- cos(-10°).· sim tan (-150°)· cos- 800°

A: 1.(sin160-cos250)/(sin330-cos(-290))     =(0.342-(-0 342))/(-0.5-0.342)   =-0.813 2.(sin233+sin2123…

Q: tan x-1 3. Which expression is equal to using identities? tan x+1 1-cot x 1+cot x cot x 1+cot x cot…

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Q: cos x- senx = cos4 x - sen x tan e tan a-1 tan a-coto (sec x + 1)(sec x-1) = tan?x

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Q: d 1 dr tan? (x)

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Q: Cos 40 x Cos 50 - Sin 40 x Sin 50.

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Q: #18. Use inverse functions where needed to find all solutions of the equation in the interval [0,…

A: We have to solve the problem

Q: sin x – 2+ csc x (c) sin x – 1 sin x CSc x sin x + 1 | 1 (d) cos(tan-l x) = V1+ x² 1+cos u (e) Using…

A: We have to answer following Questions.

Q: sec 0 tan 0 Establish the identity = sin 0 1+ tan? 0

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Q: Rewrite sin(x+π6) in terms of sinx and cosx.

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Q: 2. What is the exact value of tan (-75°)? O 2-V3 O-2+ V3 O 2+ v3 O-2-V3

A: To find :  The exact value of tan(-75°). Note: To find the exact value apply the reference angle by…

Q: tan x-1 3. tan x - 1 sin? x +3 sin x +2 4. sin x +2

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Q: sin- 33°+ sin 123°- cos(-10°)· sin 80° (4) tan (-150°) cos² 800°

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Q: Verify the identity algebraically. Use a graphing utility to check your result graphically.…

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Q: sin 20 If x = 3 sin 0, write the expression in terms of just x. 6. 9-x2 sin 3 a. 6. - -1 b. sin 3x+…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: sin 0 1- cos 0 = 2 csc 0 1 cos 0 ite the left side of the expression with sin 0(1- cos ) EGO

A: We can establish the identity as asked in the question as below

Q: cos 5x - cos 3x = -8 sin? x(2 cos3 x - cos x) Working with the left-hand side, use a Sum-to-Product…

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Q: sin 0 1 + cos 0 Establish the identity: 2 csc 0 1 + cos 0 sin 0

A: given sinθ1+cosθ+1+cosθsinθ=2cosecθ

Q: establish each identity.

A: Our Aim is to prove sin θ cos θcos2 θ-sin2 θ=tan θ1-tan2 θ -(i)

Q: sec8 0-1 tan 8 0 sec40-1 tan 20

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Q: csc(x)=3     0<x<pie/2  cos(x/2)=? sin(x/2)=? tan(x/2)=?

A: Given that: cscx=3,   0&lt;x&lt;π2

Q: Establish each identity given in attachment.

A: To establish the identity, we need to prove that the left hand side is equal to the right hand side.…

Q: sin (-0) cos² (-0) Establish the identity: cos 0 sin 0 sin (-0) - cos (-ø)

A: Given: sin2-θ-cos2-θsin-θ-cos-θ=cosθ-sinθ

Q: Different substitutionsa. Evaluate  ∫ tan x sec2 x dx using the substitution u = tan x.b. Evaluate…

A: Given: I=∫tanxsec2xdx for evaluating given integral we substitute  u=tanx…

Q: tan² x 1. Simplify: - 1+secx 2. Simplify: cot? x (sin² x) 3. Verify: sec²x cot x – cot x = tan x

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: Prove that sec2A+tan2A is equivalent to cosA+sinA/CosA-SinA Hence solve for 0 degree<=X<=360 degre…

A: We need to prove that sec2A+tan2A=cosA+sinAcosA-sinA. So,…

Q: Prove that sec2A+tan2A is equivalent to cosA+sinA/CosA-SinA Hence solve for 0 degree<=X<=360 degre…

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Q: 57 + tan 4 15. Find the EXACT value of tan 3

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Q: single trigonometric 2. Simplify sin (3x) cos (4x) + sin (4x) cos (3.x). Express your answer as a…

A: To simplify sin3x cos4x+sin4x cos3x. To express the answer as a single trigonometric function.

Q: 6. (a) Express cos (2 tan- ) (b) Express sin (2 cosx) as an algebraic expression in x. (c) Express…

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Q: a-X Differentiate Tan" 1+ ax

A: Given:- tan-1a-x1+ax To find Differentiate given function

Q: Part D

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Q: cos(x+π6)+sin(x−π3)=______

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Q: sin 0-2 sin3 0 1. 2 cos30-cose = tan O 1 2. tan? x(1+ coť x) 1-sin2x 1 3. sec ( 2 cos'x) = 2x2-1

A: we have to prove

Q: Rewrite sin(x+5π/6) in terms of sinx and cosx.

A: Given that sin(x+ 5pi/6) Write in terms of sinx and cosx

Q: Rewrite sin(x+5pi/6) in terms of sin x and cos x. Enclose arguments of functions in parentheses.

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Q: cos² 2. Simplify the expression sin² -1 2-1 O-sec² x O-tan² x O tan² x O sec² x

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Q: Simplify tan(arctan 1/3 ). 1/3 -1/3 no solution

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Q: - sin( - a) + sin-x 元 Simplify sin sin(21- x) 지+ 2

A: Given: sinπ2−x+sin(π−x)+sin3π2−x+sin(2π−x)

Q: sin (x-b) If it is known that sin (b) = - 1, It is equivalent to 1+tan²(x)' O a) cos (x) Ob) – cos…

A: Some of the important identities of trigonometry are as follows:  sin2x+cos2x=1 secx=1cosx…

Q: tan x= -4 and sin x is negative

A: Here tanx=-4we know trigonometric identity,sec2x=1+tan2xsec x=±1+tan2xsec x=±1+(-4)2sec…

Q: 1. cos(π+x) sec(-x) tan(-x) sec(27+x) sin(7+x) cot(-x) Simplify the expression- simplify every…

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Q: entity. Cos (x- 90°)- cos(x+90°) = 2 sin x COS %3D

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Q: Use inverse functions where needed to find all solutions of the equation in the interval [0, 2pi).…

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

Q: Sin 40 x Cos 20 + Sin 20 x Cos 40.

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Q: 1. If tan a = 2 then tan( a) = %3D 2. If sin z 0.1 then sin(- x): %3D 3. If cos a = 0.3 then cos(…

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Q: tan x+1 4. Consider f(x) and g(x) = sin x + cos x %3D %3D sec x a) Identify any non-permissible…

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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.