Question

sin(7π/12)-sin(5π/12)​

Answer 1

Answer:

0

Step-by-step explanation:

sin(7π/12) - sin(5π/12)

sin(π/3 + π/4) - sin(π/6 + π/4)

Since sin(A+B) = sinAcosB + cosAsinB, hence,

{sin(π/3) cos(π/4) + cos(π/3) sin(π/4)} - {sin(π/6) cos(π/4) + cos(π/6) sin(π/4)}

Now put in the values,

{(√3/2)(1/√2) + (1/2)(1/√2)} - {(1/2)(√2/2) + (√3/2)(√2/2)}

⇒ (1/√2){(√3/2) + (1/2)} - (√2/2){(√3/2) + (1/2)}

⇒ {(√3+1)/2} {(1/√2) - (√2/2)}

⇒ {(√3+1)/2} {(1/√2) - (1/√2)}

⇒ {(√3+1)/2} {0}

⇒ 0