1.

If sec x + tan x =22/7 , find the value of tanx/2A. the value of tan `(x)/(2)=(29)/(15)`B. the value of tan `(x)/(2)=(29)/(15)`C. the value of cosec x + cot `x=(29)/(15)`D. thevalue of cosec x + cot `x=(15)/(29)`

Answer» Correct Answer - B::C
`sec x + tan x = (22)/(7)`
`rArr (1+sin x)/(cos x)=(22)/(7)`
`rArr (1+(2t)/(1+t^(2)))/((1-t^(2))/(1+t^(2)))=(22)/(7)`, where `t= tan.(x)/(2)`
`rArr ((1+t)^(2))/(1-t^(2))=(22)/(7)`
`rArr (1+t)/(1-t)=(22)/(7)`
`rArr t=(15)/(29)`
Now cosec x + cot x
`=(1+cos x)/(sin x)`
`=(2 cos^(2)(x//2))/(2sin(x//2)cos(x//2))`
`=cot((x)/(2))=(29)/(15)`


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