Question

If cos A +cos2 A = 1 then sin2 A + sin 4 A is equal to​

Answer 1

Answer :-

The value of Sin²A + Sin⁴A is 1 when Cos A + Cos²A = 1.

Step-by-step explanation :-

Given :

Cos A + Cos²A = 1

To find :

Sin²A + Sin⁴A

Solution :

∅ Cos A + Cos²A = 1 can be written as 1 - Cos²A = Cos A

∅ Sin²A + Sin⁴A can be written as Sin²A + (Sin²A Sin²A)

⇒ Sin²A + (Sin²A Sin²A)

∅ Sin²A = 1 - Cos²A

⇒ Sin²A + (1 - Cos²A 1 - Cos²A)

∅ 1 - Cos²A = Cos A

⇒ Sin²A + Cos A Cos A

∅ Cos A Cos A = Cos²A

⇒ Sin²A + Cos²A

∅ Sin²A + Cos²A = 1

⇒ 1

∴ The value of Sin²A + Sin⁴A is 1.

Answer 2

Step-by-step explanation:

ANSWER ✍️

______________

• cosA+cos 2A=1
• cosA=1−cos 2 A
• cosA=sin 2A

Hence

• sin 4A+sin 2A
• cos 2A+cosA
• =1

Hope this helps you ☺️