If sin(120 - A)= sin(120 - B) and 0

Question

If sin(120 - A)= sin(120 - B) and 0< A, B < π then all values of A, B are given by. (A) A + B = (π/3) (B) A - B or A+ B = (π/3) (C) A = B (D)  A + B = 0

Tardigrade Admin · Accepted Answer

Given trigonometrical equation is sin(120 -A)= sin(120 - B) Since sine is positive in II quadrant ∴ either 120 - A = 120 - B ⇒ A = B or 120 - A = 180 -(120 -B) ⇒ 120 -A = 60 + B ⇒ A+ B = (π/3)

Q. If $sin (120 - A) = sin (120 - B)$ and $0 < A, B < π$ then all values of $A, B$ are given by.

$A + B = \frac{π}{3}$

$A - B$ or $A + B = \frac{π}{3}$

$A = B$

$A + B = 0$

Given trigonometrical equation is $sin (120 - A) = sin (120 - B)$
Since sine is positive in II quadrant
$∴$ either $120 - A = 120 - B$
$\Rightarrow A = B$
or $120 - A = 180 - (120 - B)$
$\Rightarrow 120 - A = 60 + B$
$\Rightarrow A + B = \frac{π}{3}$

Q. If sin(120−A)=sin(120−B) and 0<A,B<π then all values of A,B are given by.

A+B=3π​

A−B or A+B=3π​

A=B

A+B=0