Question

If Sin x +sin²x=1 then the value of cos²x+cos⁴x is ?

Answer 1

$\huge\underline\mathfrak{Answer-}$

$\boxed{\tt{\red{Cos^2\:x+Cos^4\:x=1}}}$

$\huge\underline\mathfrak{Explanation-}$

Given :

$\tt{Sinx+Sin^2\:x=1}$

To find :

$\tt{Value\:of\:Cos^2\:x+Cos^4\:x}$

Solution :

We know that,

$\tt{Sin^2\:x+Cos^2\:x=1}$ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀–eq (1)

Also, it is given that,

$\tt{Sinx+Sin^2\:x=1}$ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀–eq (2)

From (1) and (2),

$\implies$ $\tt{\cancel{Sin^2\:x}+Cos^2\:x}$ $\tt{=}$ $\tt{Sinx+\cancel{Sin^2\:x}}$

$\implies$ $\tt{Cos^2\:x=Sinx}$⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀–eq (3)

Squaring both sides,

$\implies$ $\tt{(Cos^2\:x)^2=(Sinx)^2}$

$\implies$ $\tt{Cos^4\:x=Sin^2\:x}$ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀–eq (4)

Adding (3) and (4),

$\implies$ $\tt{Cos^2\:x+Cos^4\:x=Sin\:x+Sin^2\:x}$

[ °•° $\tt{Sinx+Sin^2\:x=1}$ ]

•°• $\boxed{\tt{\red{Cos^2\:x+Cos^4\:x=1}}}$

Answer 2

Answer:

cos²x + cos⁴x = 1

Step-by-step explanation:

We Have :-

sinx + sin²x = 1

To Find :-

cos²x + cos⁴x

Identities Used :-

sin²x + cos²x = 1

Solution :-

sinx + sin²x = 1 ------------( i )

1 = sin²x + cos²x

sinx + sin²x = sin²x + cos²x

sinx = cos²x -----------( ii )

( sinx )² = ( cos²x )²

sin²x = cos⁴x-------------( iii )

Putting ( ii ) , ( iii ) in ( i )

we get

cos²x + cos⁴x = 1