Question

sin alpha + beta minus , gamma equal to 1 by 2 cos beta + Gamma minus Alpha equal to 1 by 2 and tan alpha + beta minus, equal to 1 find the value of alpha beta gamma

Answer 1

you mean,

$sin(\alpha+\beta-\gamma)=1\\\\cos(\beta+\gamma-\beta)=\frac{1}{2}\\\\tan(\alpha+\beta)=1$

then, we have to find $\alpha\beta\gamma$

$sin(\alpha+\beta-\gamma)=1=sin\pi/2$

$\alpha+\beta-\gamma=\pi/2$...(1)

$cos(\beta+\gamma-\beta)=\frac{1}{2}=cos\pi/3$

$\alpha+\gamma-\beta=\pi/3$.....(2)

and $tan(\alpha+\beta)=1=tan\pi/4$

or, $\alpha+\beta=\pi/4$.....(3)

from equations (1) and (3),

$\gamma=-\pi/4$.....(4)

now, from equation (2) and (4),

$\alpha-\beta=\pi/3+\pi/4=7\pi/12$.....(5)

from equations (3) and (5),

$\alpha=\frac{5\pi}{12}$

and $\beta=\frac{-\pi}{6}$

so, $\alpha\beta\gamma=\frac{5\pi}{12}.\frac{-\pi}{6}.\frac{-\pi}{4}$

= 5π³/288

Answer 2

Answer:

Refers to the attachment