Question
If sin 2 A + sin 4 A = 1 and cos
2 A + cos 4 A = 1, then find the value of (sin 4 A - cos 4 A)Solution
sin 2 A + sin 4 A = 1 -------- (I)
cos 2 A + cos 4 A = 1 ------- (II)
On subtracting equation I from II,
We get, sin 2 A + sin 4 A - cos 2 A - cos 4 A = 1 - 1
Or, sin 4 A - cos 4 A = cos 2 A - sin 2 A
Or, sin 4 A - cos 4 A = (cos A + sin A) (cos A - sin A)
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