Question

A) cos 33° cos 27° − sin 33° sin 27°; b) cos 12° cos 42° + sin 12° sin 42°; c) sin П/5 cos 3П/10 + sin 3П/10 cos П/5 d) sin 4П/9 cos П/9 - sin П/9 cos 4П/9 e) tg 19°+tg 11° / 1−tg 19° tg 11°; f) tg 72°−tg 12° / 1+tg 72° tg 12°;

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

Sure, I can help you with these trigonometric expressions. Let's go through each of them one by one:

a) cos 33° cos 27° - sin 33° sin 27°: This is the formula for the cosine of the difference of two angles: cos(A - B) = cos(A)cos(B) + sin(A)sin(B). So, in this case: cos(33° - 27°) = cos(6°) = cos(33°)cos(27°) + sin(33°)sin(27°).

b) cos 12° cos 42° + sin 12° sin 42°: Again, using the formula for the cosine of the difference of two angles. cos(42° - 12°) = cos(30°) = cos(12°)cos(42°) + sin(12°)sin(42°).

c) sin π/5 cos 3π/10 + sin 3π/10 cos π/5: This seems to be using the formula for the sine of the sum of two angles: sin(A + B) = sin(A)cos(B) + cos(A)sin(B). So, in this case: sin(π/5 + 3π/10) = sin(5π/10 + 3π/10) = sin(4π/5) = sin(π/5)cos(3π/10) + cos(π/5)sin(3π/10).

d) sin 4π/9 cos π/9 - sin π/9 cos 4π/9: This is also using the formula for the sine of the difference of two angles. sin(4π/9 - π/9) = sin(3π/9) = sin(π) = sin(4π/9)cos(π/9) - cos(4π/9)sin(π/9).

e) tan 19° + tan 11° / (1 - tan 19°tan 11°): This expression involves the formula for the tangent of the sum of two angles: tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B)). So, in this case: tan(19° + 11°) = tan(30°) = (tan(19°) + tan(11°)) / (1 - tan(19°)tan(11°)).

f) tan 72° - tan 12° / (1 + tan 72°tan 12°): This is also using the formula for the tangent of the difference of two angles. tan(72° - 12°) = tan(60°) = (tan(72°) - tan(12°)) / (1 + tan(72°)tan(12°)).

Remember to make sure your calculator is in the correct mode (degrees or radians) depending on the given angles.