Question

if sin theta + sin² theta =1 prove that cos² theta + cos⁴ theta=1


pls answer❤​

Answer 1

Step-by-step explanation:

ain²theeta + cos²theeta=1

that implies, sin²theeta = 1-cos²theta..............1

GIVEN Sin theeta+ sin²theeta=1................2

replace 1

sin theeta+1-cos²theeta = 1

that implies cos²theeta=sin theeta...........3

to prove:

cos²theeta + cos⁴theeta...............4

replace 3 in 4

that implies,

sin theeta + (sin theeta)²

from 2 we get

sin theeta +sin²theeta=1

that implies

cos²theeta + cos⁴theeta=1

Answer 2

Answer:

Step-by-step explanation:

Given, sinθ + sin²θ = 1 ,

=> sinθ = cosθ (as cos²θ+sin²θ = 1 )

=> θ = 45°

to prove cos²θ+cos⁴θ = 1

take LHS = cos²θ+cos⁴θ

= cos²45°+cos⁴45°

=

                =  $( \frac{1}{{2} } ) + ( \frac{1}{4} )$

                = $\frac{3}{4}$

                ≠ 1

contradiction  => there is some fault in the question