Question

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.....​

Answer 1

see explanation

Explanation:

sin150° = sin(180 - 150)° = sin30°

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

cos300° = cos(360 - 300)° = cos60°

sec²360° =
`(1)/(cos^2360)`

Then expressing the original gives

sin150° - tan315° + cos300° + sec²360°

= sin30° - (- tan45°) + cos60° +
`(1)/(cos^2360)`

Evaluate using exact values

=
`(1)/(2)` - (- 1) +
`(1)/(2)` +
`(1)/(1)`

=
`(1)/(2)` + 1 +
`(1)/(2)` + 1

= 3

Answer 2

9514 1404 393

Answer:

3

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