show that sin^2A + cosec^2A > 2
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L.H.S.= sin2A[sin2A] + cos2A[cos2A] /sin2Acos2A. = sin4A + cos4A/sin2Acos2A. ={ [sin2 A + cos2A]2/ sin2Acos2A } - {2sin2Acos2A/ sin2Acos2A}. = 1/sin2Acos2A - 2. = sec2 .
Aakriti001:
Apply a.m>=g.m
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sin^2a + cosec^2a
= (sin^2a - cosec^2a)^2 + 2*sin^2a*cosec^2a
=(sin^2a - cosec^2a)^2 + 2
=2 + (sin^2a - cosec^2a)^2
now the value of (sin^2a - cosec^2a) can be positive or negative or zero.
so, the minimum value of 2 + (sin^2a - cosec^2a)^2 is 2
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I Hope it's help you.... !!! :))
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sin^2a + cosec^2a
= (sin^2a - cosec^2a)^2 + 2*sin^2a*cosec^2a
=(sin^2a - cosec^2a)^2 + 2
=2 + (sin^2a - cosec^2a)^2
now the value of (sin^2a - cosec^2a) can be positive or negative or zero.
so, the minimum value of 2 + (sin^2a - cosec^2a)^2 is 2
__________________
__________________
I Hope it's help you.... !!! :))
A.M>=G.M
Sin^2A+Cosec^2A/2 >=(sin^2A×cosec^2A)^1/2
Sin^2A+Cosec^2A>=2
bri iska answere infinity he
How
sin 90 = 1 and cosec 90 = 1/sin 90 = 1
For any value of sin a, the cosec a increases tremendously.
sin 30 = 0.5, cosec 30 = 1/0.5 = 2. So sin^2 30 + cosec^2 30 = 0.25 + 4 = 4.25
sin 0 = 0, cosec 0 = infinity. So sin^2 0 + cosec^2 0 =infinity.
For any value of sin a, the cosec a increases tremendously.
sin 30 = 0.5, cosec 30 = 1/0.5 = 2. So sin^2 30 + cosec^2 30 = 0.25 + 4 = 4.25
sin 0 = 0, cosec 0 = infinity. So sin^2 0 + cosec^2 0 =infinity.
But (infinity)>2 also..
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