Explanation

(cos47-sin47)^2 = 1-sin94 = 2-k^2, and since cos47 < sin47 the difference is negative: cos47-sin47 = -sqrt(2-k^2). Thus cos^2(47)-sin^2(47) = k*(cos47-sin47) = -k*sqrt(2-k^2) - option (B). Numerically, cos47 ~= 0.682 and sin47 ~= 0.731 give cos^2-sin^2 ~= -0.0698, matching -k*sqrt(2-k^2).