1.

If sinx+co secx+tany=4 whre x and y in[0,(pi)/(2)] then tan""(y)/(2) is a root of the equation.

Answer»

`a^(2)+2alpha+1=0`
`a^(2)+2a=0`
`2a^(2)-2a-1=0`
`a^(2)-alpha-1=0`

Solution :`TAN A-tanB=(1)/(2)`
`rArr(TANA)/(1)=(COTB)/(2)=gamma`(SAY)
`rArr tan A=gamma` and `tan B=(1)/(2lambda)`
`therefore (5-3cos 2A)(5-3cos2B)`
`=[5-(3(1-lambda^(2)))/((1+lambda^(2)))]xx[5-(3(1-(1)/(4lambda^(2))))/((1+(1)/(4lambda^(2))))]`


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