Question

If sin A + sin²A = 1, then cos²A + cos⁴A =​

Answer 1

• cos²A + Sin²A = 1
• cos²A = 1 - sin²A
• such that ,
• sinA = 1 - sin²A
• then ,
• sinA = cos²A
• then , sub in cos²A + cos⁴A , we get
• (sinA) ²+ ( sinA ) ⁴
• = [sinA + sin²A ] ² = (1)² = 1
• Value of cos²A + cos⁴A = 1

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Answer 2

Step-by-step explanation:

Given:-

Sin A + Sin^2 A = 1

To find:-

Value of cos^2 A + cos^4 A ?

Solution:-

Given that

Sin A + Sin^2 A = 1

=> Sin A = 1 - Sin^2 A

We know that

Sin^2 A + Cos^2 A = 1

=> Sin A = Cos^2 A --------(1)

Now The value of Cos^2 A + Cos^4 A

=> Cos^2 A + Cos^2 A × Cos^2 A

From (2) we have

=> Sin A + Sin A × Sin A

=> Sin A + Sin^2 A

=> 1

Answer:-

The value of Cos^2 A + Cos^4 A is 1

Used formulae:-

• Sin^2 A + Cos^2 A = 1