Question

State whether the following statement is true or false: if sin x = 1/2 ; then sin 2 x = 1 ​

Answer 1

`\\ \sf\longmapsto sinx=(1)/(2)`

`\\ \sf\longmapsto sinx=sin30`

`\\ \sf\longmapsto x=30`

Now

`\\ \sf\longmapsto sin2x=1`

`\\ \sf\longmapsto sin2x=sin90`

`\\ \sf\longmapsto 2x=90`

`\\ \sf\longmapsto x=(90)/(2)`

`\\ \sf\longmapsto x=45`

Hence its false

Answer 2

• False

Explanation:

• sin x = 1/2 ⇒ x = 30°
• sin 2x = 1 ⇒ 2x = 90° ⇒ x = 45°

The answer is false as 30° ≠ 45°