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given A=sin^2a+cos^4a,then for value of a,(a=theta)

pallavi pradeep bhardwaj , 16 Years ago

Grade 12

1 Answers

Jitender Singh

Ans:Hello student, please find answer to your question
$A = sin^{2}a + cos^{4}a$
$A = sin^{2}a + cos^{2}a.cos^{2}a$
$A = sin^{2}a + cos^{2}a(1-sin^{2}a)$
$A = sin^{2}a + cos^{2}a-sin^{2}a.cos^{2}a$
$A = 1-sin^{2}a.cos^{2}a$
$A = 1-\frac{4}{4}.sin^{2}a.cos^{2}a$
$4A = 4-(2sina.cosa)^{2}$
$4A = 4-(sin2a)^{2}$
$(sin2a)^{2} = 4-4A$
$(sin2a)^{2} = 4(1-A)$
$sin2a = \pm2\sqrt{1-A}$
$sin^{-1}sin2a = sin^{-1}(\pm2\sqrt{1-A})$
$2a = sin^{-1}(\pm2\sqrt{1-A})$
$a =\frac{1 }{2}.sin^{-1}(\pm2\sqrt{1-A})$

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