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`        the maximum value of the expression 1/sin^2a+3sinacosa+5cos^2a`
7 years ago

```							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

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```
7 years ago
```							Dear Smit,
Sanatan is right!! Its the right answer.
```
7 years ago
```							cosec^2(a)+5(cos^2(a))
```
7 years ago
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