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the maximum value of the expression 1/sin^2a+3sinacosa+5cos^2a
multiply the numerator and the denominator by 2
numerator will become 2 &
the denominator = 2sin^2a+6sinacosa+10cos^2a
taking a (sin^2a + cos^2a) aside we get
= sin^2a +6sinacosa +9cos^2a +sin^2a + cos^2a
= (sina + 3 cosa)^2 + sin^2a +cos^2a
= (sina + 3 cosa)^2 + 1
now the expression becomes 2/( (sina + 3 cosa)^2 + 1 )
for the maximum value of the expression the denominator must be minimum
and for denominator to be minimum , (sina + 3 cosa)^2 must be minimum
the minimum value of , (sina + 3 cosa)^2 can be zero when tana = -3
therefore the maximum value of the expression 2/( (sina + 3 cosa)^2 + 1 ) = 2/( 0 +1 )
= 2
if you want to aprreciate the solution , please click below on approve.
Dear Smit,
Sanatan is right!! Its the right answer.
cosec^2(a)+5(cos^2(a))
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