Trigonometryhard · Past Paper
If tan theta + sin theta = m and tan theta - sin theta = n, then m^2 - n^2 is:
A4 sqrt(mn)
B2 sqrt(mn)
Csqrt(mn)
D4mn
✓ Correct Answer: A — 4 sqrt(mn)
m^2 - n^2 = (m+n)(m-n) = (2 tan)(2 sin) = 4 tan sin. Also sqrt(mn) = sqrt(tan^2 - sin^2) = sqrt(sin^2/cos^2 - sin^2) = sin/cos sqrt(1-cos^2) = tan sin.
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