Solve - sinA^4+cosA^4+1=2sinA^2

Asked by Nganesh101 | 2nd Jan, 2020, 11:48: AM

Expert Answer:

To solve: sin4A+cos4A+1=2sin2A
sin to the power of 4 A plus cos to the power of 4 A plus 1 equals 2 sin squared A
rightwards double arrow sin to the power of 4 A plus cos to the power of 4 A plus 1 equals sin squared A plus sin squared A
rightwards double arrow sin to the power of 4 A plus cos to the power of 4 A plus 1 equals sin squared A plus 1 minus cos squared A
rightwards double arrow sin to the power of 4 A plus cos to the power of 4 A equals sin squared A minus cos squared A
rightwards double arrow sin squared A open parentheses sin squared A minus 1 close parentheses plus cos squared A open parentheses cos squared A plus 1 close parentheses equals 0
rightwards double arrow sin squared A cos squared A plus cos squared A open parentheses cos squared A plus 1 close parentheses equals 0
rightwards double arrow cos squared A open parentheses sin squared A plus cos squared A plus 1 close parentheses equals 0
rightwards double arrow 2 cos squared A equals 0
rightwards double arrow 1 plus cos 2 A equals 0
rightwards double arrow A equals fraction numerator cos to the power of negative 1 end exponent open parentheses negative 1 close parentheses over denominator 2 end fraction equals straight pi over 2

Answered by Renu Varma | 6th Jan, 2020, 01:04: PM