Question

 (Sin 30°+cos 60°)-(sin 60° + cos 30°) is equal to:

(a) 0
(b) 1+2√3
(c) 1-√3
(d) 1+√3

​

Answer 1

(c) $1-\sqrt{3}$

(sin30° + cos60°) - (sin60° + cos30°) = 1 - √3

Step-by-step explanation:

Here, (sin30° + cos60°) - (sin60° + cos30°)

= $\dfrac{1}{2}+\dfrac{1}{2})-(\dfrac{\sqrt{3}}{2}+\dfrac{\sqrt{3}}{2})$

= $\dfrac{1+1}{2}-\dfrac{\sqrt{3}+\sqrt{3}}{2}$

= $\dfrac{2}{2}-\dfrac{2\sqrt{3}}{2}$

= $1-\sqrt{3}$

Extra:

Here, (sin30° + cos60°) - (sin60° + cos30°)

= sin30° + cos60° - sin60° - cos30°

= sin30° + cos(90° - 30°) - sin60° - cos(90° - 60°)

= sin30° + sin30° - sin60° - sin60°

• since cos(90° - A) = sinA

= 2 (sin30° - sin60°)

= $2(\dfrac{1}{2}-\dfrac{\sqrt{3}}{2})$

= 1 - √3

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Answer 2

Step-by-step explanation:

check the image for answer