Question

Sin²150°+cos²120°-tg²150°

Answer 1

Ответ:

$\bold { \frac{1}{6} }$

Объяснение:

sin²150° + cos²120° - tg²150° = $\bold { \frac{1}{6} }$

sin150° = $\frac{1}{2}$

cos120° = $-\frac{1}{2}$

tg150° = $-\frac{\sqrt{3} }{3}$

$(\frac{1}{2} )^{2} + (-\frac{1}{2} )^{2} - (-\frac{\sqrt{3} }{3} )^{2} = \frac{1}{4} + \frac{1}{4} - \frac{3}{9} = \frac{9 + 9 - 12}{36} = \frac{6}{36} = \bold { \frac{1}{6} }$

Answer 2

To calculate the given expression, let's break it down step by step:

1. sin²150°: The sine of 150° is equal to 1/2. Therefore, sin²150° = (1/2)² = 1/4.

2. cos²120°: The cosine of 120° is equal to -1/2. Therefore, cos²120° = (-1/2)² = 1/4.

3. tan²150°: The tangent of 150° is equal to -√3. Therefore, tan²150° = (-√3)² = 3.

Now we can substitute these values into the original expression:

sin²150° + cos²120° - tan²150°

= 1/4 + 1/4 - 3

= 1/2 - 3

= -5/2

Therefore, sin²150° + cos²120° - tan²150° = -5/2.