Question

Find all the solutions on the interval [0,2π).

sin[x+ π 4 ]+sin[x− π 4 ] = −1

Can you please also show all the steps on how you solved this I am having a hard time understanding this concept.

Answer 1

• sin(a+b)+sin(a-b)=2sinacosb

now

• sin(x+π/4)+sin(x-π/4)=-1
• 2sinxcosπ/4=-1
• 2sinx(1/√2)=-1
• √2sinx=-1
• sinx=-1/√2

Solution is

• -45° or -π/4
• -135° or -3π/4
• 225°

225° is most suitable because it has accurate value -1/√2.

-π/4 is the principal value

Answer 2

hope this helps

.look it once