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value of $a,b$ in trigonometric expression

Ration of sum and Product of Trigonometric expression.Value of $sec^2 a+2sec^2 b$Finding value of $k$ in trigonometric equation.Finding smallest positive root $sqrtsin(1-x)=sqrtcos x$Trigonometric series sum involving tangentsFind all integers $m$ and $n$ such that $ncosfracpim= sqrt8+sqrt32+sqrt768$If $cos^4 alpha+4sin^4 beta-4sqrt2cos alpha sin beta +2=0$, then find $alpha$, $beta$ in $(0,fracpi2)$value of $x$ in Trigonometric equationTrigonometric series sum with $sin$ functionfinding wired trigononetric ratio

1

$begingroup$

If $a,b$ are positive integers such that $displaystyle sqrt8+sqrt32+sqrt768=acosbigg(fracpibbigg)$

what i try: i am trying to convert it into $displaystyle sqrt2+2cos 8x=sqrt2cos 4x$

How do i solve it Help me please

trigonometry

share|cite|improve this question

asked Mar 12 at 10:09

jackyjacky

1,186715

$endgroup$

add a comment | 

1

$begingroup$

If $a,b$ are positive integers such that $displaystyle sqrt8+sqrt32+sqrt768=acosbigg(fracpibbigg)$

what i try: i am trying to convert it into $displaystyle sqrt2+2cos 8x=sqrt2cos 4x$

How do i solve it Help me please

trigonometry

share|cite|improve this question

asked Mar 12 at 10:09

jackyjacky

1,186715

$endgroup$

add a comment | 

$begingroup$

If $a,b$ are positive integers such that $displaystyle sqrt8+sqrt32+sqrt768=acosbigg(fracpibbigg)$

what i try: i am trying to convert it into $displaystyle sqrt2+2cos 8x=sqrt2cos 4x$

How do i solve it Help me please

trigonometry

share|cite|improve this question

asked Mar 12 at 10:09

jackyjacky

1,186715

$endgroup$

share|cite|improve this question

asked Mar 12 at 10:09

jackyjacky

1,186715

share|cite|improve this question

asked Mar 12 at 10:09

jackyjacky

1,186715

asked Mar 12 at 10:09

jackyjacky

1,186715

asked Mar 12 at 10:09

jackyjacky

1,186715

2 Answers
2

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oldest

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4

$begingroup$

You're on the right track. The surd is $$2sqrt2(1+sqrt2+sqrt3)=2sqrt2(1+sqrt2(1+costfracpi6))=2sqrt2(1+2costfracpi12)=4costfracpi24.$$So take $a=4,,b=24$.

share|cite|improve this answer

edited Mar 12 at 11:30

answered Mar 12 at 10:21

J.G.J.G.

30.3k23148

$endgroup$

add a comment | 

3

$begingroup$

Hint: Your term is equal to $$2sqrt2+2sqrt2+sqrt3$$

share|cite|improve this answer

edited Mar 12 at 10:23

J.G.

30.3k23148

answered Mar 12 at 10:21

Dr. Sonnhard GraubnerDr. Sonnhard Graubner

77.8k42866

$endgroup$

add a comment | 

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4

$begingroup$

You're on the right track. The surd is $$2sqrt2(1+sqrt2+sqrt3)=2sqrt2(1+sqrt2(1+costfracpi6))=2sqrt2(1+2costfracpi12)=4costfracpi24.$$So take $a=4,,b=24$.

share|cite|improve this answer

edited Mar 12 at 11:30

answered Mar 12 at 10:21

J.G.J.G.

30.3k23148

$endgroup$

add a comment | 

4

$begingroup$

You're on the right track. The surd is $$2sqrt2(1+sqrt2+sqrt3)=2sqrt2(1+sqrt2(1+costfracpi6))=2sqrt2(1+2costfracpi12)=4costfracpi24.$$So take $a=4,,b=24$.

share|cite|improve this answer

edited Mar 12 at 11:30

answered Mar 12 at 10:21

J.G.J.G.

30.3k23148

$endgroup$

add a comment | 

$begingroup$

You're on the right track. The surd is $$2sqrt2(1+sqrt2+sqrt3)=2sqrt2(1+sqrt2(1+costfracpi6))=2sqrt2(1+2costfracpi12)=4costfracpi24.$$So take $a=4,,b=24$.

share|cite|improve this answer

edited Mar 12 at 11:30

answered Mar 12 at 10:21

J.G.J.G.

30.3k23148

$endgroup$

share|cite|improve this answer

edited Mar 12 at 11:30

answered Mar 12 at 10:21

J.G.J.G.

30.3k23148

answered Mar 12 at 10:21

J.G.J.G.

30.3k23148

answered Mar 12 at 10:21

J.G.J.G.

30.3k23148

3

$begingroup$

Hint: Your term is equal to $$2sqrt2+2sqrt2+sqrt3$$

share|cite|improve this answer

edited Mar 12 at 10:23

J.G.

30.3k23148

answered Mar 12 at 10:21

Dr. Sonnhard GraubnerDr. Sonnhard Graubner

77.8k42866

$endgroup$

add a comment | 

3

$begingroup$

Hint: Your term is equal to $$2sqrt2+2sqrt2+sqrt3$$

share|cite|improve this answer

edited Mar 12 at 10:23

J.G.

30.3k23148

answered Mar 12 at 10:21

Dr. Sonnhard GraubnerDr. Sonnhard Graubner

77.8k42866

$endgroup$

add a comment | 

$begingroup$

Hint: Your term is equal to $$2sqrt2+2sqrt2+sqrt3$$

share|cite|improve this answer

edited Mar 12 at 10:23

J.G.

30.3k23148

answered Mar 12 at 10:21

Dr. Sonnhard GraubnerDr. Sonnhard Graubner

77.8k42866

$endgroup$

share|cite|improve this answer

edited Mar 12 at 10:23

J.G.

30.3k23148

answered Mar 12 at 10:21

Dr. Sonnhard GraubnerDr. Sonnhard Graubner

77.8k42866

edited Mar 12 at 10:23

J.G.

30.3k23148

edited Mar 12 at 10:23

J.G.

30.3k23148

answered Mar 12 at 10:21

Dr. Sonnhard GraubnerDr. Sonnhard Graubner

77.8k42866

answered Mar 12 at 10:21

Dr. Sonnhard GraubnerDr. Sonnhard Graubner

77.8k42866