Trigonometryhard · Past Paper
If tan^2 theta = 1 - e^2, find sec theta + tan^3 theta * cosec theta.
A(2 - e^2)^(3/2)
B(1 - e^2)^(3/2)
C2 - e^2
De^3
✓ Correct Answer: A — (2 - e^2)^(3/2)
sec + (sin^3/cos^3)(1/sin) = sec + sin^2/cos^3 = (cos^2+sin^2)/cos^3 = 1/cos^3 = sec^3. sec^2 = 1+tan^2 = 2-e^2. So sec^3 = (2-e^2)^(3/2).
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