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Prove the following:
`cos ((3pi)/ 2 + x ) cos(2pi + x) [cot ((3pi)/2 - x) + cot (2pi + x)]= 1`
Concept: undefined >> undefined
Prove the following:
sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x
Concept: undefined >> undefined
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Prove the following:
`cos ((3pi)/4 + x) - cos((3pi)/4 - x) = -sqrt2 sin x`
Concept: undefined >> undefined
Prove the following:
sin2 6x – sin2 4x = sin 2x sin 10x
Concept: undefined >> undefined
Prove the following:
cos2 2x – cos2 6x = sin 4x sin 8x
Concept: undefined >> undefined
Prove the following:
sin 2x + 2sin 4x + sin 6x = 4cos2 x sin 4x
Concept: undefined >> undefined
Prove the following:
cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)
Concept: undefined >> undefined
Prove the following:
`(cos9x - cos5x)/(sin17x - sin 3x) = - (sin2x)/(cos 10x)`
Concept: undefined >> undefined
Prove the following:
`(sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x`
Concept: undefined >> undefined
Prove the following:
`(sin x - siny)/(cos x + cos y)= tan (x -y)/2`
Concept: undefined >> undefined
Prove the following:
`(sin x + sin 3x)/(cos x + cos 3x) = tan 2x`
Concept: undefined >> undefined
Prove the following:
`(sin x - sin 3x)/(sin^2 x - cos^2 x) = 2sin x`
Concept: undefined >> undefined
Prove the following:
`(cos 4x + cos 3x + cos 2x)/(sin 4x + sin 3x + sin 2x) = cot 3x`
Concept: undefined >> undefined
Prove the following:
cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1
Concept: undefined >> undefined
Prove the following:
`tan 4x = (4tan x(1 - tan^2 x))/(1 - 6tan^2 x + tan^4 x)`
Concept: undefined >> undefined
Prove the following:
cos 4x = 1 – 8sin2 x cos2 x
Concept: undefined >> undefined
Prove the following:
cos 6x = 32 cos6 x – 48 cos4 x + 18 cos2 x – 1
Concept: undefined >> undefined
Prove that: `(cos x + cos y)^2 + (sin x - sin y )^2 = 4 cos^2 (x + y)/2`
Concept: undefined >> undefined
Prove that: `(cos x - cosy)^2 + (sin x - sin y)^2 = 4 sin^2 (x - y)/2`
Concept: undefined >> undefined
Prove that: sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x
Concept: undefined >> undefined
