Question

Solve for $x$ and $y$:
$4^{sinx}+3^{\frac{1}{cosy}}=11$
${5.16}^{sinx}-{2.3}^{\frac{1}{cosy}}=2$

Answer 1

To solve for x and y

Given equations are

$4^{sinx}+3^{\frac{1}{cosy}}=11$

${5.16}^{sinx}-{2.3}^{\frac{1}{cosy}}=2$

Let ,
$4^{sinx}=a$

$3^{\frac{1}{cosy}}=b$

On Putting these value ,equations becomes

$a+b=11$
$5a^2-2b=2$

On Adding both equations , we get

$5a^2+2a-24=0$

On solving this equation , we get
$a=2anda=-24/10$

Here ,
$4^{sinx}=-24/10$ is not Possible
Therefore , we take
$4^{sinx}=2$

$sinx=\frac{1}{2}$

$x=\frac{\Pi }{6}$
On Putting this value , we get

$a+b=11$
$2+b=11$

$b=9$

$3^{\frac{1}{cosy}}=9$

$cosy=\frac{-1}{2}$

$y=\frac{2\Pi }{3}ory=\frac{-\Pi }{3}$

Hence ,
$x=\frac{\Pi }{6}and$

$y=\frac{2\Pi }{3}$