Chứng minh các đẳng thức sau:

a) sin605° = sin(3.180° + 65°) = ‒sin65°.

sin1645° = sin(9.180° + 25°) = ‒sin25° = ‒sin(90° ‒ 65°) = ‒cos65°.

cot25° = cot(90° ‒ 65°) = tan65°.

sin2605° + sin21645° + cot225°

= (‒sin65°)2 + (‒cos65°)2 + (tan65°)2

= 1 + tan265°

=1cos265∘

b) sin530° = sin(3.180° ‒ 10°) = sin10°.

sin640° = sin(4.180° ‒ 80°) = ‒sin80° = ‒sin(90° ‒ 10°) = ‒cos10°.

sin530°1+sin640°=sin10°1−cos10°=sin210°sin10°1−cos10°

=1−cos210°sin10°1−cos10°=1+cos10°1−cos10°sin10°1−cos10°

=1+cos10°sin10°=111sin10°+cot10° .