Question

If Sin A + Sin²A = 1, Prove that Cos²A + Cos⁴A = 1 ​

Answer 1

Answer:

Step-by-step explanation:

Given , sinA + sin²A = 1

To prove , cos²A + cos⁴A = 1

Now ,

sinA + sin²A = 1

=> sinA = 1 - sin²A

=> sinA = cos²A [ °•° sin²∅ + cos²∅ = 1 ]

=> ( sinA )² = ( cos²A )² [ • squaring both sides ]

=> sin²A = cos⁴A

=> 1 - cos²A = cos⁴A [ °•° sin²∅ + cos²∅ = 1 ]

=> cos⁴A + cos²A = 1 [ Hence Proved ]

Answer 2

Step-by-step explanation:

Sin A + Sin^2 A =1

Sin A = 1 - Sin^2 A

Sin A = Cos^2 A. [Sin^2 A+ Cos^2 A =1]

Now,

Cos^2 A +Cos^4 A = 1

From LHS

Cos^2 A + (cos^2 A)^2

= Cos^2 A + (Sin A)^2

= Cos^2 A + Sin^2 A

=1. [Sin^2 A + Cos^2 A = 1]

= RHS

since, LHS = RHS

Hence , proved.