Question

Difficulty: EasyBasic Trigonometric Ratios, Special Angles, and Identities

What is the numerical value of 4sin30+2cos60tan454\sin 30^\circ + 2\cos 60^\circ - \tan 45^\circ?

Answer: 2

Answer

2
Substituting the exact trigonometric values for special angles into the expression gives 4(12)+2(12)1=2+11=24\left(\frac{1}{2}\right) + 2\left(\frac{1}{2}\right) - 1 = 2 + 1 - 1 = 2.

Step-by-Step Solution

1
Recall exact values for special trigonometric angles
sin30=12\sin 30^\circ = \frac{1}{2}, cos60=12\cos 60^\circ = \frac{1}{2}, and tan45=1\tan 45^\circ = 1
These are standard special angle values derived from standard right-angled triangles.
2
Substitute the values into the original expression
4(12)+2(12)1=2+114\left(\frac{1}{2}\right) + 2\left(\frac{1}{2}\right) - 1 = 2 + 1 - 1
Direct algebraic substitution.
3
Simplify the resulting numerical expression
2
Combining terms 2+112 + 1 - 1 gives 22.

Key Concept

Basic Trigonometric Ratios and Special Angles
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