Question

pls answer pls no unnecessary answers ( this is a model paper class 12 ) any maths genius pls​

Answer 1

Answer:

here is the answer

Step-by-step explanation:

pls mark as brainliest

Answer 2

Answer:

Step-by-step explanation:

We have,

$\tt{cos^{-1}(x)+cos^{-1}(y)+cos^{-1}(z)=\pi}$

$\sf{\implies\,cos^{-1}(x)+cos^{-1}(y)=\pi-cos^{-1}(z)}$

$\sf{\implies\,cos^{-1}(xy-\sqrt{1-x^2}\,\cdot\,\sqrt{1-y^2})=cos^{-1}(-z)}$

$\sf{\implies\,cos^{-1}\{xy-\sqrt{(1-x^2)(1-y^2)}\,\}=cos^{-1}(-z)}$

$\sf{\implies\,xy-\sqrt{(1-x^2)(1-y^2)}=-z}$

$\sf{\implies\,xy+z-\sqrt{(1-x^2)(1-y^2)}=0}$

$\sf{\implies\,xy+z=\sqrt{(1-x^2)(1-y^2)}}$

$\sf{\implies\,(xy+z)^2=\{\sqrt{(1-x^2)(1-y^2)}\,\}^2}$

$\sf{\implies\,x^2y^2+z^2+2xyz=(1-x^2)(1-y^2)}$

$\sf{\implies\,x^2y^2+z^2+2xyz=1-x^2-y^2+x^2y^2}$

$\sf{\implies\,z^2+2xyz=1-x^2-y^2}$

$\sf{\implies\,x^2+y^2+z^2+2xyz=1}$