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sin(150°) - tan(315°) + cos(300°) + sec^2 (360°)

I know it's answer is 3 but I don't understand how ...

please explain it in detailed steps pls.....​

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sqdancefan

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Answer:

  3

Step-by-step explanation:

If you need to, you can use your calculator to evaluate this expression. Or, you can make use of your knowledge of trig function values.

  sin(150°) = sin(30°) = 1/2

  tan(315°) = tan(-45°) = -tan(45°) = -1

  cos(300°) = cos(-60°) = cos(60°) = 1/2

  sec(360°) = sec(0°) = 1

Then the expression evaluates to ...

  1/2 -(-1) +1/2 +1² = 3

Ver imagen sqdancefan

Answer:

see explanation

Step-by-step explanation:

sin150° = sin(180 - 150)° = sin30°

tan315° = - tan(360 - 315)° = - tan45°

cos300° = cos(360 - 300)° = cos60°

sec²360° = [tex]\frac{1}{cos^2360}[/tex]

Then expressing the original gives

sin150° - tan315° + cos300° + sec²360°

= sin30° - (- tan45°) + cos60° + [tex]\frac{1}{cos^2360}[/tex]

Evaluate using exact values

= [tex]\frac{1}{2}[/tex] - (- 1) + [tex]\frac{1}{2}[/tex] +[tex]\frac{1}{1}[/tex]

= [tex]\frac{1}{2}[/tex] + 1 + [tex]\frac{1}{2}[/tex] + 1

= 3

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