Question

If sinΘ + sin2Θ = 1, then cos2Θ + cos4Θ = 1 ?​

Answer 1

Answer:

hey liya,

Step-by-step explanation:

Given : sin θ + sin2 θ = 1 ⇒ sin θ = 1 – sin2 θ Taking LHS = cos2θ + cos4θ = cos2 θ + (cos2 θ)2 = (1– sin2 θ) + (1– sin2 θ)2 …(i) Putting sin θ = 1 – sin2 θ in Eq. (i), we get = sin θ + (sin θ)2 = sin θ + sin2 θ = 1 [Given: sin θ + sin2 θ = 1] = RHS Hence ProvedRead more on Sarthaks.com - https://www.sarthaks.com/930499/if-sin-sin-2-1-then-prove-that-cos-2-1-cos-4-1

Answer 2

$\huge\boxed{\fcolorbox{green}{pink}{Answer}}$

$\huge\bold\pink{Given:}$

sin θ + sin² θ = 1

⇒ sinθ = 1 – sin² θ

$\bold\green{Taking\:LHS}$

= cos²θ + cos⁴θ

= cos² θ + (cos⁴ θ)²

= (1– sin² θ) + (1– sin² θ)² ....(1)

$\bold\red{putting\:sinθ\: = \: 1 \:– \:sin² θ\:in\:eq\:....(1)\:}$

= sin θ + (sin θ)²

= sin θ + sin² θ

= 1

[Given: sin θ + sin² θ = 1]

$\huge\bold\orange{RHS\:hence\:proved}$