Question

if sinx+sin²x=1 then show that cos²x+cos⁴=1
answer asappp guys plzzz​

Answer 1

Step-by-step explanation:

sinx + sin^2x = 1 1.

sinx = 1- sin^2x

sinx = cos^2x 2.

Squaring:

sin^2x = cos^4 3.

From 1 ( Substituting the values of 2. and 3.) we get:

sinx + sin^2x = 1

cos^2x + cos^4x = 1

Answer 2

The required result is proved below

Step-by-step explanation:

Given : $\sin x + \sin ^2x = 1$

To prove: $\cos ^2x+ \cos^4 x= 1$

As given

$\sin x + \sin ^2x = 1 -----(i)$

Now by trigonometric identities as we know

$\sin^2 x+ \cos^2 x = 1\\\\\Rightarrow \sin^2 x= 1-\cos^2 x$

Substitute the value in (i) we get

$\sin x +1- \cos ^2x = 1\\\\\Rightarrow \sin x - \cos ^2x = 0\\\\\Rightarrow \sin x = \cos ^2x$

Squaring both side we get

$\Rightarrow \sin^2 x= (cos^2x)^2\\\\\Rightarrow \sin^2 x= cos^4x\\\\\Rightarrow 1-\cos^2 x= cos^4x \\\\\Rightarrow \cos^2 x+ cos^4x=1$

Hence proved

#Learn more

If sinx + cosx=a then show that (sinx-cosx) =√2-a²

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