Question

If Sin x = Cos² x , Then write The value of Cos²x ( 1 + cos²x )​

Answer 1

Answer:

cos² x ( 1 + cos² x )​  = 1

Step-by-step explanation:

Given ;

sin x = cos² x

we know

cos² x  =  1 - sin² x

sin x = 1 - sin² x

sin² x  + sin x - 1 = 0

Using Sridharacharya method ;

$\displaystyle{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}\\\\\\\displaystyle{x=\dfrac{-1\pm\sqrt{1^2-4\times1\times-1}}{2\times1}}\\\\\\\displaystyle{x=\dfrac{-1\pm\sqrt{5}}{2}}$

Now ,

cos² x ( 1 + cos² x )​

⇒  sin x  ( 1 + sin x )

⇒  sin x +  sin² x

$\displaystyle{\implies\left(\dfrac{-1\pm\sqrt{5}}{2}\right)}+\left(\dfrac{-1\pm\sqrt{5}}{2}\right)^2}}$

[ Taking plus only we get ]

$\displaystyle{\implies\left(\dfrac{-1+\sqrt{5}}{2}\right)}+\left(\dfrac{-1+\sqrt{5}}{2}\right)^2}}$

On solving this we get

$\displaystyle{\implies\left(\dfrac{2\sqrt{5}-2+6-2\sqrt{5}}{4}\right)}\\\\\\\displaystyle{\implies\left(\dfrac{4}{4}\right)}\\\\\\\displaystyle{\implies 1 }$

Thus we get answer 1 .

Answer 2

Answer:

Refer to the attachment......✨✨