Question

Find the value of 45^ 30^ + 60^ 45^ - 5 90^2 0^

• A. -12
• B. 0
• C. 12
• D. 1

Hint:

Always keep a clear mental visualization of the standard trigonometric table handy during exams. Evaluating reciprocal ratios like and by converting them directly into standard and mentally ensures you never accidentally flip values under stress!

Answer 1

The Correct Option is A

Concept: This question requires substituting standard trigonometric values for common angles:

• 45^ = 1

• 30^ = 1 30^ = 2

• 60^ = 1 60^ = 2

• 45^ = 1

• 90^ = 1

• 0^ = 1

Step 1: Substitute the specific numerical trigonometric constant values into the given expression. The target expression is: \[ \text{Expression} = \frac{\tan 45^{\circ}}{\csc 30^{\circ}} + \frac{\sec 60^{\circ}}{\cot 45^{\circ}} - \frac{5\sin 90^{\circ}}{2\cos 0^{\circ}} \] Substituting the known standard values: \[ \text{Expression} = \frac{1}{2} + \frac{2}{1} - \frac{5(1)}{2(1)} \]

Step 2: Simplify the arithmetic terms. \[ \text{Expression} = \frac{1}{2} + 2 - \frac{5}{2} \]

Step 3: Group and combine the fractional terms with a common denominator of 2. \[ \text{Expression} = \left(\frac{1}{2} - \frac{5}{2}\right) + 2 \] \[ \text{Expression} = \left(\frac{1 - 5}{2}\right) + 2 \] \[ \text{Expression} = \left(\frac{-4}{2}\right) + 2 \] \[ \text{Expression} = -2 + 2 = 0 \] *Note: Let's carefully re-evaluate the expressions from image 5.* Let's double-check the calculation: 12 + 2 - 52 = 2.5 - 2.5 = 0. Thus, the value evaluates exactly to 0, matching Option (B).