Question

if sin theta +sin2 theta =1 prove that cos2theta +cod4 theta =1​

Answer 1

Answer:

1

Step-by-step explanation:

=> sinA + sin²A = 1 → sinA = 1 - sin²A

=> sinA = cos²A → sin²A = cos⁴A

Thus,

=> cos²A + cos⁴A

=> sinA + sin²A

=> 1

Answer 2

Solution :

It is given that ,

⠀⠀⠀⠀⠀• sin θ + sin²Θ = 1

sin θ = 1 - sin²Θ

we know that,

• 1 - sin²Θ = cos²Θ

So,

sin θ = cos²Θ ........(1)

We need to prove that ,cos²Θ + cos⁴Θ = 1

LHS :

›› cos²Θ + (cos²Θ)²

›› cos²Θ + sin²Θ ⠀⠀[from eq.(1) ]

• cos²Θ + sin²Θ = 1

›› 1 = RHS

⠀⠀⠀⠀LHS = RHS

Hence Proved

━━━━━━━━━━━━━━━━━━━━━━━━━

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Done࿐