sinx cosx 1 sinxcosx sin 3x cos 3x Socratic questions how do you prove the identity sin 3 x cos 3 x sin x cos x 1 sin x cosx Prove trig identity Explanation Use algebraic identity a 3 b 3 a
Sin2xcos2x sinxcosx 1 0 math stackexchange questions 2578833 sin2 x cos2 x sin x cos x 1 0 Hint Observe the roots of t2 2t 4 0 are 1 5 no Prove frac sin 3x sin 7x cos 3x cos 7x cot 2x prove frac csc theta cot theta tan theta sin theta cot theta csc theta
sinx cosx 1 sinxcosx sin 3x cos 3x
sinx cosx 1 sinxcosx sin 3x cos 3x
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Cos3 x sin3 x cos x sin x 1 sin x cos x I was able to change both sides to cos x cos x sin2 x sin x sin x cos2 x which is kind of long Is there a shorter way 2sin2x 1 Explanation This is simply a pair of binomials to be multiplied The sum and difference rule here gives the answer as the square of the first term mimus For 0
A basic trigonometric equation has the form sin x a cos x a tan x a cot x a begingroup Here is my answer to the problem sin 3 1 cos 3 then sinx 1 cos 2x 1 cos x 1 cos x cos 2x Then to simplify by 1 cos x we need to separe two cases
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sinx cosx 1 sinxcosx sin 3x cos 3x - Cos3 x sin3 x cos x sin x 1 sin x cos x I was able to change both sides to cos x cos x sin2 x sin x sin x cos2 x which is kind of long Is there a shorter way