Answer:
Step-by-step explanation:
To evaluate the expression: 1 2 2 tan² 45° cos² 30° X (sin² 30° + 4 cot² 45° - sec² 60°), we need to follow the order of operations (PEMDAS/BODMAS) and evaluate the expression step by step.
Let's break down the expression and evaluate each part:
tan² 45°: The tangent of 45° is equal to 1, so tan² 45° = 1² = 1.
cos² 30°: The cosine of 30° is equal to (√3)/2, so cos² 30° = (√3/2)² = 3/4.
sin² 30°: The sine of 30° is equal to 1/2, so sin² 30° = (1/2)² = 1/4.
cot² 45°: The cotangent of 45° is equal to 1, so cot² 45° = 1² = 1.
sec² 60°: The secant of 60° is equal to 2, so sec² 60° = 2² = 4.
Now, let's substitute these values back into the original expression:
1 2 2 (1) (3/4) X (1/4 + 4(1) - 4)
Simplifying further:
1 2 2 (3/4) X (1/4 + 4 - 4)
1 2 2 (3/4) X (1/4)
1 2 2 (3/16)
Multiplying:
1 2 (6/16)
1 (12/16)
Finally, simplifying:
3/4
Therefore, the value of the expression 1 2 2 tan² 45° cos² 30° X (sin² 30° + 4 cot² 45° - sec² 60°) is 3/4.
