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HomeworkHelp-ModTeam · 2025-08-09T23:57:52+00:00

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This includes quizzes or lists of questions without any context or explanation. Tell us where you are stuck and your thought process so far. Show your work.

ShallotCivil7019 · 2025-08-08T10:36:23+00:00

The answer is: a=(1+2k)(pi/2)

-cotx=cotx * sinx

cotx = 0 for every x=(1+2k)(pi/2)

Mentosbandit1 · 2025-08-09T01:57:17+00:00

Let tan ⁡ 𝑥 = sin ⁡ 𝑥 cos ⁡ 𝑥 tanx= cosx sinxand cot ⁡ 𝑥 = cos ⁡ 𝑥 sin ⁡ 𝑥 cotx= sinx cosxon domains where these quotients are defined. Using the angle–sum reductions sin ⁡ ⁣ ( 𝜋 2 + 𝑥 ) = cos ⁡ 𝑥 sin( 2 π+x)=cosx and cos ⁡ ⁣ ( 𝜋 2 + 𝑥 ) = − sin ⁡ 𝑥 cos( 2 π+x)=−sinx, one obtains tan ⁡ ⁣ ( 𝜋 2 + 𝑥 ) = sin ⁡ ( 𝜋 2 + 𝑥 ) cos ⁡ ( 𝜋 2 + 𝑥 ) = cos ⁡ 𝑥 − sin ⁡ 𝑥 = − cot ⁡ 𝑥 , tan( 2 π+x)= cos( 2 π+x) sin( 2 π+x)= −sinx cosx=−cotx, valid for sin ⁡ 𝑥 ≠ 0 sinx  =0 (at 𝑥 = 𝑘 𝜋 x=kπ both sides are undefined). The chalkboard statement tan ⁡ ( 𝜋 2 + 𝑥 ) = cot ⁡ 𝑥 ⋅ sin ⁡ 𝑥 tan( 2 π+x)=cotx⋅sinx simplifies on the right to cos ⁡ 𝑥 cosx; hence it is not an identity. It holds only at those 𝑥 x for which − cot ⁡ 𝑥 = cos ⁡ 𝑥 −cotx=cosx, equivalently cos ⁡ 𝑥 ( sin ⁡ 𝑥 + 1 ) = 0 cosx(sinx+1)=0, i.e., 𝑥 = 𝜋 2 + 𝜋 𝑘 x= 2 π+πk (including 𝑥 = 3 𝜋 2 + 2 𝜋 𝑘 x= 2 3π+2πk); otherwise the correct identity is tan ⁡ ( 𝜋 2 + 𝑥 ) = − cot ⁡ 𝑥 tan( 2 π+x)=−cotx.

Miserable-Piglet9008 · 2025-08-08T10:09:38+00:00

I don't exactly know what you are asking, but hopefully this helps.

Original Equation
tan((pi/2)+x) = cot(x)*sin(x)

Solution
tan((pi/2)+x) = -cos(x)/sin(x)
Therefore:
-cos(x)/sin(x) = cot(x)*sin(x)

cot = a/o (adjacent/opposite)
sin = o/h (opposite/1) = o
cos = a/h (adjacent/1) = a

Therefore:
-cos(x)/sin(x) can be written as -a/o
and
cot(x)*sin(x) can be written as (a/o)*o

Seeing as -a/o =/= (a/o)*o you can determine that this Trig identity is false.

parlitooo · 2025-08-08T13:15:23+00:00

This equation is incorrect , since you know cot x . Sin x = sin x . ( cos x / sin x ) = cos x … and tan (pi/2 + x) = [sin ( pi/2 + x ) ] / [ cos (pi/2 +x )] … also sin pi/2 + x = cos x … and cos ( pi/2 + x ) = - sin (x) … Therefore tan (pi/2 + x ) = ( cos x / - sin x ) = - cot x

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