According to Napier’s Rules of circular parts for a right angled triangle, sine of middle part equals the product of A. Tangents of two adjacent parts B. Sines of two adjacent parts C. Cosines of two adjacent parts D. Both (A) and (B) above

The correct answer is: D. Both (A) and (B) above

Napier’s Rules of Circular Parts

are a set of rules that can be used to find the trigonometric ratios of any angle in a right triangle. The rules state that the sine of the middle part of a right triangle is equal to the product of the tangents of the two adjacent parts, and the cosine of the middle part is equal to the product of the sines of the two adjacent parts.

For example, in the right triangle below, the sine of the angle $\theta$ is equal to the product of the tangents of the angles $A$ and $B$, and the cosine of the angle $\theta$ is equal to the product of the sines of the

angles $A$ and $B$.

[asy]
unitsize(1 cm);

draw((0,0)–(4,0)–(2,2.82843)–cycle);

label(“$A$”, (0,0), S);
label(“$B$”, (4,0), N);
label(“$\theta$”, (2,2.82843), E);

draw((0,0)–(2,0));
draw((2,0)–(2,2.82843));

label(“$1$”, (1,0), S);
label(“$1$”, (2,1), E);
[/asy]

Therefore, the answer to the question is: D. Both (A) and (B) above