Use the identities to find csc(x) and cos(x) if tan(x) =6 and cos(x)

Q: Verify the identity. (Simplify at each step.) sin1/2 x cos x - sin5/2 x cos x = cos³ x/ sin x sin /2…

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Q: cos x + + sin x |

A: Given:cosx+π2+sinx-π2=2   Formula:  sinA±B=sinAcosB ± cosAsinB......(1) cosA±B=cosAcosB ∓…

Q: complete the identity cos x-sin x/cos x+ sin x-cos x/sin x

A: Here we use basic trigonometric relations to complete the given identity.

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

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Q: Verify the identity. csc(x) cos²(x) + sin(x) = csc(x)

A: The given identity is cscxcos2x+sinx=cscx.

Q: Verify that sin(x+y) + sin(x-y) = 2sin(x)cos(y). You must list out each step you used to verify this…

A: we know that sinC+sinD=2sinC+D2cosC-D2 here, C≡x+y, D≡x-y

Q: Verify the identity. cos3 x sin2 x = (sin2 x − sin4 x)cos x

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Q: 2+tan x cos³ x

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Q: Verify the identity     sec x + tan x = cos x /(1 − sin x) .

A: Our Aim is to prove the trigonometric identity given below:- sec x + tan x = cos x /(1 − sin x)…

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: Find tan(x) and sin(x) if sec(x)=3 and cos(x) >0

A: It is given that,  sec(x)=3 and cos(x)>0 we have to find ,  tan(x), sin(x)

Q: Verify the identity: tan x/2 = (sec x - 1)/tan x

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Q: 1. Verify the identity. Show all steps. sin x tan² x-sin x = tan x (tan x – 1) cos x sin x+cos x

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Establish the identity: csc θ x tan θ= sec θ

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Q: Simplify (cos x- sinx)(cosx+ sinx) sin x cos'x cos x 2 cos x- 1 2 cos x+ 1

A: Given expression, cosx-sinxcosx+sinx

Q: Verify the identity: sin x/(1 + cos x) = (1 - cos x)/sin x.

A: sinx1+cosx=sinx1+cosx×1-cosx1-cosx=sinx1-cosx1-cos2x     ∵a+ba-b=a2-b2=sinx1-cosxsin2x…

Q: Prove the identity: csc 0 x tan 0 = sec 0

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Q: Verify the identity: tan(-x)cos x = -sin x

A: To verify:      tan(-x)cos x = -sin x We will start from LHS and will try to get RHS.

Q: Evaluate f (2 cos x-sin x)² sin x

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Q: Use an identity to solve the equation tan x - sec x = 1 on the interval [0, 2π).

A: The given equation is tanx-secx=1.

Q: Verify the identity: tan x + 1/tan x = 1/(sin x cos x)

A: To verify: tan x+1tan x=1sinx. cosx

Q: a. [CO²2 2 cos²x√4 tan x tan² x da

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Q: csc(x)=7  sin(x/2)=? cos(x/2)=? tan(x/2)=

A: Given that: csc(x)=7

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: Verify the identity: tan x csc x cos x = 1

A: Known facts: tanx=sinxcosxcscx=1sinx

Q: 3) f(x) = cos5 (tan (sin²(x*))) ||

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Q: Verify the identity: csc x cos2 x + sin x = csc x.

A: the given identity is: cscx cos2x+sinx=cscx we have to verify the identity.

Q: 2 csc x 1+ cos x 1- cos x

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

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Q: Establish the identity sec x - cos x= sin x tam x

A: GivenTo establish the identitysec x-cos x=sin x tan xFormula:sin2 θ+ cos2 θ=1sin θcos θ=tan θsec…

Q: Verify the identity: csc x - csc x cos2 x = sin x

A: We know that, cosecx=1sinx            ⋯⋯1sin2x+cos2x=1sin2x=1-cos2x     ⋯⋯2 We have,…

Q: Verify the identity. Show your work below. (cos x + sin x)² = 2 cos x sinx+1

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

A: Given identity, cscx-cosxcotx=sinx

Q: sin x+ tan x sin (2x) 5. Determine the non-permissible values of the identity 1+ cos x 2 cos x Cos3x…

A: Solve using properties trigonometric identities

Q: Verify the identity. (Simplify at each step.) cos³ x sin“ x = (sin“ x – sin6 x)cos x cos³ x sin4 x =…

A: We will solve the problem.

Q: Verify the identity. (Simplify at each step.) cos³ x sin4 x = (sin4 x — sin6 x)cos x cos³ x sin4 x =…

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Q: cos 2x cos.x+ sin x xp-

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Q: Verify the identity. (Simplify at each step.) 8 cos (w/2) - x] sin (ca/2) – x] 8 cos (1/2) – x sin…

A: Explanation of the answer is as follows

Q: Find cos x if tan x= -(2 √2)/2 and sin x= √6/3

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Q: Verify the identity: sin x tan x + cos x = sec x.

A: Given:sinx tanx+cosx=secx

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: • tan°(x) Xp- cos“(x) 1 1 tan9

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Q: Find sin(x/2) =  cos(x/2) =  tan(x/2) =  Given cos(x) = -24/25, 180 degrees < x < 270 degrees

A: topic - half angle values of trigonometric functions

Q: Solve for x in the equation: arc tan (x + 1) + arc tan (x – 1) = arc tan (12)

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Q: cos (x2 + 3x +5 ) COS

A: Solved below

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.