Question

Is sin 15 x cos 15 rational?

Answer 1

sin15°
=sin(45°-30°)
=sin45°cos30°-cos45°sin30°
=1/√2×√3/2-1/√2×1/2
=(√3-1)/2√2  and
cos15°
=cos(45°-30°)
=cos45°cos30°+sin45°sin30°
=1/√2×√3/2+1/√2×1/2
=(√3+1)/2√2
∴, sin15°×cos15°
=(√3-1)/2√2×(√3+1)/2√2
=(√3-1)(√3+1)/8
={(√3)²-(1)²}/8
=2/8
=1/4 which is a rational number.

Answer 2

yes .......... sin 15 x cos 15 rational