(sin 3x + sin x) sin x + (cos 3x - cos ...

(sin 3x + sin x) sin x + (cos 3x - cos x) cos x =0

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(sin3x + sin x) sin x + (cos3x-cos x) cos x = 0

Prove that: (sin3x+sin x)sin x+(cos3x-cos x)cos x=0

Knowledge Check

The general solution of sin x -3 sin 2x+ sin 3x= cos x-3 cos 2x +cos 3x is

A

`n pi +(pi)/(8)`

B

`(n pi)/(2)+(pi)/(8)`

C

`(-1)^(n) (n pi)/(2)+(pi)/(8)`

D

`2 n pi + cos^(-1) ""(3)/(2)`

The general solution of sinx - 3 sin 2 x + sin 3x = cos x - 3cos 2x + cos 3 x is

A

`npi +pi//8`

B

`npi //2 + pi//8`

C

`(-1)^n (n pi//2) + (pi//8)`

D

`2 npi + cos^(-1) (3//2)`

The general solution of sinx - 3 sin 2x + sin3x = cos x - 3 cos 2x + cos 3x is.

A

`npi+(pi)/(8)`

B

`(npi)/(2)+(pi)/(8)`

C

`(-1)^(n)(npi)/(2)+(pi)/(8)`

D

`2npi+cos^(-1)((3)/(2))`

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Explore conceptually related problems

(sin x + sin 3x)/(cos x - cos 3x) = ?

Solve sin x-3 sin 2x + sin 3x = cos x -3 cos 2x + cos 3x .

(sin x + sin 3x + sin 5x)/(cos x + cos 3x + cos 5x) = tan 3x

(sin x + sin3x + sin5x) / (cos x + cos3x + cos5x) = tan3x

Some examples Type: 1 (1) (sin5A-sin3A)/(cos5A+cos3A)=tan A(2)(sin3x+sin x)sin x+(cos3x-cos x)cos x=0 (3) Prove that cot4x(sin5x+sin3x)=cot x(sin5x-sin3x)

RS AGGARWAL-TRIGONOMETRIC , OR CIRCULAR, FUNCTIONS-Exercise (15C)

(sin x + sin 3x)/(cos x - cos 3x) = ?
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(sin 7x - sin 5x)/(cos 7x + cos 5x) = tan x
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(sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x
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(cos 9x - cos 5x)/(sin 17x - sin 3x) = (-sin 2x)/(cos 10x)
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(sin x + sin 3x + sin 5x)/(cos x + cos 3x + cos 5x) = tan 3x
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(( sin 7x + sin 5x)+(sin 9x + sin 3x))/((cos 7x + cos 5x)+(cos 9x+ cos...
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Prove that: cot" "4x" "(s in" "5x" "+" "s in" "3x)" "=" "cot" "x" "(s ...
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(sin 3x + sin x) sin x + (cos 3x - cos x) cos x =0
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Prove that: (cosx-cosy)^2+(sinx-siny)^2=4sin^2(x-y)/2
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(sin 2x - sin 2y)/(cos 2y-cos 2x) = cot (x+y)
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(cos x + cosy)/(cos y -cos x) = cot ((x+y)/(2)) cot ((x-y)/(2))
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(sinx+siny)/(sinx-siny)=tan((x+y)/2)*cot((x-y)/2)
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Prove that: s in" "3x" "+" "s in" "2x" "" "s in" "x" "=" " 4" "s in" "...
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(cos 4x sin 3x -cos 2x sin x )/(sin 4x sin x+ cos 6x cos x)= tan 2x
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(cos 2x sin x + cos 6x sin 3x)/(sin 2x sin x + sin 6x sin 3x) =cot 5x
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The value of sin 10^(@) sin 30^(@) sin 50^(@) sin 70^(@) is
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sin 20^(@) sin 40^(@) sin 60^(@) sin 80^(@) =(3)/(16)
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cos 10^(@) cos 30^(@) cos 50^(@) cos 70^(@) =(3)/(16)
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If cos x + cos y =(1)/(3) and sin x + sin y=(1)/(4) prove that tan...
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Prove that (i) " 2 cos " 45^(@) " cos " 15^(@)=((sqrt(3)+1))/(2) "...
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