Materi Trigonometri. -Jawab dengan menggunakan cara-

[tex]\displaystyle 2\sin35\sin10=2\sin35\cdot2\sin5\cos5\\2\sin35\sin10=2\cos5\cdot2\sin35\sin5\\2\sin35\sin10=2\cos5(\cos30-\cos40)\\2\sin35\sin10=\cos5(\sqrt3-2\cos40)\\2\sin35\sin10=\sqrt3\cos5-2\cos40\cos5\\\\\frac{\sec5}{2}\cdot\sin10=\frac{1}{2\cos5}\cdot2\sin5\cos5\\\frac{\sec5}{2}\cdot\sin10=\sin5\\\\\frac{\cos40}{\sin5}\cdot\sin10=\frac{\cos40}{\sin5}\cdot2\sin5\cos5\\\frac{\cos40}{\sin5}\cdot\sin10=2\cos40\cos5[/tex]

[tex]\displaystyle 2\sin35\sin10-\frac{\cos40\sin10}{\sin5}=\sqrt3\cos5-2\cos40\cos5-2\cos40\cos5\\2\sin35\sin10-\frac{\cos40\sin10}{\sin5}=\sqrt3\cos5-4\cos40\cos5\\2\sin35\sin10-\frac{\cos40\sin10}{\sin5}=\sqrt3\cos5-2\left(\frac12\sqrt2+\cos35\right)\\2\sin35\sin10-\frac{\cos40\sin10}{\sin5}=\sqrt3\cos5-2\left(\frac12\sqrt2+\frac12\sqrt3\cos5-\frac12\sin5\right)[/tex]
[tex]\displaystyle 2\sin35\sin10-\frac{\cos40\sin10}{\sin5}=\sqrt3\cos5-(\sqrt2+\sqrt3\cos5-\sin5)\\2\sin35\sin10-\frac{\cos40\sin10}{\sin5}=\sqrt3\cos5-\sqrt2-\sqrt3\cos5+\sin5\\2\sin35\sin10-\frac{\cos40\sin10}{\sin5}=-\sqrt2+\sin5\\\\2\sin35\sin10-\frac{\cos40\sin10}{\sin5}-\frac{\sec5\sin10}{2}=-\sqrt2+\sin5-\sin5\\2\sin35\sin10-\frac{\sec5\sin10}{2}-\frac{\cos40\sin10}{\sin5}=-\sqrt2\\-2\sqrt2\left(2\sin35\sin10-\frac{\sec5\sin10}{2}-\frac{\cos40\sin10}{\sin5}\right)=-2\sqrt2(-\sqrt2)[/tex]
[tex]\displaystyle \boxed{\boxed{-2\sqrt2\sin10\left(2\sin35-\frac{\sec5}{2}-\frac{\cos40}{\sin5}\right)=4}}[/tex]

-2√2 sin 10° (2 sin 35° - (sec 5°)/2 - (cos 40°)/(sin 5°))

= -4√2 sin 10° sin 35° + √2 sin 10° sec 5° + 2√2 sin 10° cos 40° / (sin 5°)

= 2√2 . -2 sin 35° sin 10° + √2 . (2 sin 5° cos 5°) . 1/(cos 5°) +
2√2 (2 sin 5° cos 5°) cos 40° / (sin 5°)

= 2√2 (cos (35° + 10°) - cos (35° - 10°)) + 2√2 sin 5° +
2√2 . 2 cos 40° cos 5°

= 2√2 (cos 45° - cos 25°) + 2√2 sin 5° +
2√2 (cos (40° + 5°) + cos (40° - 5°))

= 2√2 (1/2 √2 - cos 25°) + 2√2 sin 5° + 2√2 (cos 45° + cos 35°)

= 2 - 2√2 cos 25° + 2√2 sin 5° + 2 + 2√2 cos 35°
= 2 + 2 + 2√2 (cos 35° - cos 25° + sin 5°)
= 4 + 2√2 (-2 sin (35° + 25°)/2 sin (35° - 25°)/2 + sin 5°)
= 4 + 2√2 (-2 sin 30° sin 5° + sin 5°)
= 4 + 2√2 (-2 . 1/2 . sin 5° + sin 5°)
= 4 + 2√2 (0)
= 4