Question

5sin pi/6 + 3tg pi/4 - cos pi/4 - 10tg pi/4

Answer 1

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Answer 2

To simplify the expression, let's first convert the trigonometric functions to their corresponding values:

• sin(pi/6) = 1/2
• tg(pi/4) = 1
• cos(pi/4) = √2 / 2

Now, substitute these values into the expression:

5 * (1/2) + 3 * 1 - √2 / 2 - 10 * 1

Now, perform the operations step by step:

= 5/2 + 3 - √2 / 2 - 10

Next, find a common denominator to combine the fractions:

The common denominator for 2 and √2 is 2√2.

= (5 * √2 + 6 - √2 - 20 * 2√2) / 2√2

= (5 * √2 - √2 - 12√2) / 2√2

= (5 - 1 - 12)√2 / 2√2

= (-8)√2 / 2√2

Now, the √2 terms cancel out:

= -8 / 2

= -4

So, the simplified value of the expression is -4.