Question

if sinθ + sin²θ=1, Prove that cos²θ + cos⁴θ = 1

Answer 1

Answer:

Step-by-step explanation:

LHS :

sin theta = 1 - sin^2 theta        ( sin^2 theta + cos^2 theta = 1 )

sin theta = cos^2 theta

cos^2 theta + ( sin theta ) ^2

cos^2 theta + sin^2 theta = 1

1 = 1

LHS = RHS

hence proved

Answer 2

$\huge\bf\purple{\mathfrak{Given:-}}$

→ sinθ + sin²θ = 1

To prove :-

→ cos²θ +cos⁴θ = 1

Proof:-

→ sinθ + sin²θ = 1

→ sinθ = 1 - sin²θ

→ sinθ = cos²θ [ 1- sin²θ= cos²θ]

Squaring on both side

→ sin²θ = cos⁴θ

→ 1 - cos²θ = cos⁴θ [ sin²θ= 1- cos²θ]

→ 1 = cos⁴θ + cos²θ

→ cos⁴θ + cos²θ = 1

$\therefore \: \boxed{ \tt{proved!}}$