Trig1.5

Eliminate from  and

By rule of cross-multiplication from the given equations,we get

$\frac{\cos\theta}{bc_1-b_1c}=\frac{\sin\theta}{ca_1-c_1a}=\frac{1}{ab_1-a_1b}\,$

$\cos\theta=\frac{bc_1-b_1c}{ab_1-a_1b},\sin\theta=\frac{ca_1-c_1a}{ab_1-a_1b}\,$

From $\cos^2 \theta+\sin^2 \theta=1,[\frac{bc_1-b_1c}{ab_1-a_1b}]^2+[\frac{ca_1-c_1a}{ab_1-a_1b}]^2=1\,$

Simplifying

$(bc_1-b_1c)^2+(ca_1-c_1a)^2=(ab_1-a_1b)^2\,$

Hence in the given equations, $\theta\,$ is eliminated.