A strange trigonometric identityProving a trigonometric identityWhich trigonometric identities involve trigonometric functions?A trigonometric identityProve this trigonometric identityTrigonometric Identity SymmetryProve $sin^2 theta +cos^4 theta =cos^2 theta +sin^4 theta $How many points to prove a trigonometric identity?What are the practical applications of this trigonometric identity?Help! Cubic trigonometric Identity proofWhat proves this trigonometric identity $cos2 theta=cos^2theta-sin^2theta$?
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A strange trigonometric identity
Proving a trigonometric identityWhich trigonometric identities involve trigonometric functions?A trigonometric identityProve this trigonometric identityTrigonometric Identity SymmetryProve $sin^2 theta +cos^4 theta =cos^2 theta +sin^4 theta $How many points to prove a trigonometric identity?What are the practical applications of this trigonometric identity?Help! Cubic trigonometric Identity proofWhat proves this trigonometric identity $cos2 theta=cos^2theta-sin^2theta$?
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In this paper, equation (4.5), the authors state the trigonometic identity
$$
sinleft( fracnpi 1-theta right) = (-1)^n sinleft( fracnpi theta1-thetaright)
$$
Nothing like it is on Wikipedia's list of trigonometric identities. How can we prove this?
trigonometry
asked Jun 6 at 12:53
user14717user14717
3,94011 silver badges20 bronze badges
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add a comment |
$begingroup$
In this paper, equation (4.5), the authors state the trigonometic identity
$$
sinleft( fracnpi 1-theta right) = (-1)^n sinleft( fracnpi theta1-thetaright)
$$
Nothing like it is on Wikipedia's list of trigonometric identities. How can we prove this?
trigonometry
asked Jun 6 at 12:53
user14717user14717
3,94011 silver badges20 bronze badges
$endgroup$
$begingroup$
It probably uses: $1- frac11-theta= fractheta1-theta$ so it's shifting by $pi$
$endgroup$
– dbx
Jun 6 at 13:00
add a comment |
$begingroup$
In this paper, equation (4.5), the authors state the trigonometic identity
$$
sinleft( fracnpi 1-theta right) = (-1)^n sinleft( fracnpi theta1-thetaright)
$$
Nothing like it is on Wikipedia's list of trigonometric identities. How can we prove this?
trigonometry
asked Jun 6 at 12:53
user14717user14717
3,94011 silver badges20 bronze badges
$endgroup$
In this paper, equation (4.5), the authors state the trigonometic identity
$$
sinleft( fracnpi 1-theta right) = (-1)^n sinleft( fracnpi theta1-thetaright)
$$
Nothing like it is on Wikipedia's list of trigonometric identities. How can we prove this?
trigonometry
trigonometry
asked Jun 6 at 12:53
user14717user14717
3,94011 silver badges20 bronze badges
asked Jun 6 at 12:53
user14717user14717
3,94011 silver badges20 bronze badges
asked Jun 6 at 12:53
user14717user14717
3,94011 silver badges20 bronze badges
asked Jun 6 at 12:53
user14717user14717
3,94011 silver badges20 bronze badges
asked Jun 6 at 12:53
user14717user14717
3,94011 silver badges20 bronze badges
3,94011 silver badges20 bronze badges
$begingroup$
It probably uses: $1- frac11-theta= fractheta1-theta$ so it's shifting by $pi$
$endgroup$
– dbx
Jun 6 at 13:00
add a comment |
$begingroup$
It probably uses: $1- frac11-theta= fractheta1-theta$ so it's shifting by $pi$
$endgroup$
– dbx
Jun 6 at 13:00
$begingroup$
It probably uses: $1- frac11-theta= fractheta1-theta$ so it's shifting by $pi$
$endgroup$
– dbx
Jun 6 at 13:00
$begingroup$
It probably uses: $1- frac11-theta= fractheta1-theta$ so it's shifting by $pi$
$endgroup$
– dbx
Jun 6 at 13:00
add a comment |
1 Answer
1
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votes
$begingroup$
Hint:
Just write
$$sinleft( fracnpi 1-theta right) =sinleft( fracnpi(1-theta + theta) 1-theta right) = sinleft(npi + fracnpitheta1-theta right) $$
Now, apply the addition formula for $sin(alpha + beta)$.
answered Jun 6 at 12:58
trancelocationtrancelocation
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint:
Just write
$$sinleft( fracnpi 1-theta right) =sinleft( fracnpi(1-theta + theta) 1-theta right) = sinleft(npi + fracnpitheta1-theta right) $$
Now, apply the addition formula for $sin(alpha + beta)$.
answered Jun 6 at 12:58
trancelocationtrancelocation
16k1 gold badge10 silver badges30 bronze badges
$endgroup$
add a comment |
$begingroup$
Hint:
Just write
$$sinleft( fracnpi 1-theta right) =sinleft( fracnpi(1-theta + theta) 1-theta right) = sinleft(npi + fracnpitheta1-theta right) $$
Now, apply the addition formula for $sin(alpha + beta)$.
answered Jun 6 at 12:58
trancelocationtrancelocation
16k1 gold badge10 silver badges30 bronze badges
$endgroup$
add a comment |
$begingroup$
Hint:
Just write
$$sinleft( fracnpi 1-theta right) =sinleft( fracnpi(1-theta + theta) 1-theta right) = sinleft(npi + fracnpitheta1-theta right) $$
Now, apply the addition formula for $sin(alpha + beta)$.
answered Jun 6 at 12:58
trancelocationtrancelocation
16k1 gold badge10 silver badges30 bronze badges
$endgroup$
Hint:
Just write
$$sinleft( fracnpi 1-theta right) =sinleft( fracnpi(1-theta + theta) 1-theta right) = sinleft(npi + fracnpitheta1-theta right) $$
Now, apply the addition formula for $sin(alpha + beta)$.
answered Jun 6 at 12:58
trancelocationtrancelocation
16k1 gold badge10 silver badges30 bronze badges
answered Jun 6 at 12:58
trancelocationtrancelocation
16k1 gold badge10 silver badges30 bronze badges
answered Jun 6 at 12:58
trancelocationtrancelocation
16k1 gold badge10 silver badges30 bronze badges
answered Jun 6 at 12:58
trancelocationtrancelocation
16k1 gold badge10 silver badges30 bronze badges
16k1 gold badge10 silver badges30 bronze badges
add a comment |
add a comment |
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$begingroup$
It probably uses: $1- frac11-theta= fractheta1-theta$ so it's shifting by $pi$
$endgroup$
– dbx
Jun 6 at 13:00