Question

FindA and B if, 2 sin(90° - (2A - B)} = 1 and 3 cot{90° - (A + B)) = 1​

Answer 1

The value of $A$ is $26.14$ and $B$ is $-7.71$

Step-by-step explanation:

Given,

$2 sin(90-(2A - B)) = 1$ and $3 cot(90-(A + B)) =1$

∴ $2 sin(90-(2A - B)) = 1$

⇒$cos(2A-B)=\frac{1}{2}$ (∵ $sin(90-\theta)=cos\theta$ )

⇒$cos(2A-B)=cos60$ (∵$cos60=\frac{1}{2}$)

⇒$2A-B=60$__1

And, $3 cot(90-(A + B)) =1$

⇒$tan(A+B)=\frac{1}{3}$

⇒$(A+B)=tan^{-1}\frac{1}{3}$

⇒$A+B=18.43$__2

Adding equation-1 and 2,

$3A=(60+18.43)$

⇒$A=\frac{78.43}{3}$

⇒$A=26.14$

Plug the value of $A$ in equation-2,

$26.14+B=18.43$

⇒$B=(18.43-26.14)$

⇒$B=-7.71$

So, The value of $A$ is $26.14$ and $B$ is $-7.71$