Trigonometryhard · Past Paper
Simplify: (sin^4 A - cos^4 A + 1) cosec^2 A
A1
B2
Csin^2 A
Dcos^2 A
✓ Correct Answer: B — 2
sin^4 - cos^4 = (sin^2-cos^2)(sin^2+cos^2) = sin^2 - cos^2. Then sin^2 - cos^2 + 1 = sin^2 + sin^2 = 2 sin^2. Multiplied by cosec^2, it becomes 2.
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