Question

Prove that
I) 2 sin²Ab+ cos⁴A = 1 + sin4A

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Answer 1

$\huge\sf\color{lightblue}{\bigstar\: Correct\:Question\:\bigstar}$

Pʀᴏᴠᴇ Tʜᴀᴛ :-

I) 2 sin²A+ cos⁴A = 1 + sin⁴A

$\huge\sf\color{lightblue}{\bigstar\: Solutions\:\bigstar}$

$\purple{➱ \:2 sin²A \:+ \:cos⁴A}$

$\purple{➱2 sin²A\: +\: [1\:-\:sin²A]²}$

$\purple{\:➱2sin²A + 1+sin⁴A-2sin²A}$

$\purple{➱1\:+\:sin⁴A}$

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LHS = RHS

${2sin²A + cos⁴A = 1 + sin⁴A}$

✯ ʜᴇɴᴄᴇ, Pʀᴏᴠᴇᴅ

Answer 2

Pʀᴏᴠᴇ Tʜᴀᴛ :-

I) 2 sin²A+ cos⁴A = 1 + sin⁴A

$\huge\sf\color{purple}{\bigstar\: Solutions\:\bigstar}$

$\red{➱ \:2 sin²A \:+ \:cos⁴A}$

$\red{➱2 sin²A\: +\: [1\:-\:sin²A]²}$

$\red{\:➱2sin²A + 1+sin⁴A-2sin²A}$

$\red{➱1\:+\:sin⁴A}$

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LHS = RHS

{2sin²A + cos⁴A = 1 + sin⁴A}2sin²A+cos⁴A=1+sin⁴A

ItzJanhvi 10❤