Question

if sin A + sin²A=1 then cos²A+cos⁴A=?​

Answer 1

Answer:

If sinA + sin²A = 1, prove that cos²A + cos⁴A = 1. Good question, Here is your answer! Hence LHS = RHS, proved

Answer 2

$sinA+sin2A=1</p><p>or, sin^{2} A = 1-sinAsin2A=1−sinA -----------------(1)</p><p>And,</p><p>        cos^{2} A+ cos^{4} A = 1- sin^{2} A+ ( cos^{2}A) ^{2}cos2A+cos4A=1−sin2A+(cos2A)2</p><p>                                                  =1- sin^{2} A+ [(1-sin^{2}A)] ^{2}=1−sin2A+[(1−sin2A)]2</p><p>                                                 =1- sin^{2}A + {[1-(1- sinA)]} ^{2}=1−sin2A+[1−(1−sinA)]2</p><p>                                                 =1- sin^{2} A+ sin^{2} A=1−sin2A+sin2A</p><p>                                                  = 1$

If sinA + sin²A = 1, prove that cos²A + cos⁴A = 1. Good question, Here is your answer! Hence LHS = RHS, proved.