Question

If sinA + sin²A = 1, prove that cos²A + cos⁴A = 1.

Answer 1

If sinA + sin²A = 1, prove that cos²A + cos⁴A = 1.

Good question,

Here is your answer!

=) sinA + sin²A = 1

=) sinA = 1 - sin²A

=) sinA = cos²A

Put its value in cos²A + cos⁴A,

=) cos²A + (cos²A)²

=) cos²A + sin²A

=) 1

Hence LHS = RHS, proved.

Answer 2

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 ]

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Hope it helps !!