Question

Prove that sin (π/4+ x) + sin (π/4 – x) = √2 cos x.​

Answer 1

Answer:

Since we know that

• Sin(A+B)+Sin(A-B)=2SinACosB
• so,
• 2Sinπ/4CosX
• 2×1/√2CosX
• √2 CosX
• Hope it will help you please mark me as brainliest

Answer 2

Step-by-step explanation:

sin(π/4+X) + sin(π/4-X)

=[{sin(π/4)×cosX}+{cos(π/4)×sinX}] +

[{sin(π/4)×cosX}-{cos(π/4)×sinX}]

=2{sin(π/4)×cosX}

=2{(1/√2)×cosX}

=2×1/√2cosX

=√2cosX