For 0 lt x le (pi)/(2), show that x - (x...

For `0 lt x le (pi)/(2)`, show that `x - (x^(3))/(6) lt sin x `

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Let y = (tan x)^(sinx) for 0 lt x lt (pi)/(2) . If (dy)/(dx)= (tan x)^(sinx) (( cos x ) log (tan x ) + g(x)) then g(x) =

sin x `sec^(2) x `

sec x cosec x

sec x

cosec x

If 0 lt x lt (pi)/(2) , then find tan ((pi)/(4)+ (x)/(2) ) + tan ((pi)/(4) - (x)/(2) )

` 2 sec x`

`2 cos x`

` sec x`

`cos x`

If 0 lt alpha lt beta lt gamma lt (pi)/(2) , then the equation (x- sin beta)(x- sin gamma) +(x- sin alpha) (x- sin gamma) + (x- sin alpha) (x-sin beta) = 0 has

real and unequal roots

non-real roots

real and equal roots

real and unequal roots greater than 2.

For `0 lt x le (pi)/(2)`, show that `x - (x^(3))/(6) lt sin x `

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Let y = (tan x)^(sinx) for 0 lt x lt (pi)/(2) . If (dy)/(dx)= (tan x)^(sinx) (( cos x ) log (tan x ) + g(x)) then g(x) =

If 0 lt x lt (pi)/(2) , then find tan ((pi)/(4)+ (x)/(2) ) + tan ((pi)/(4) - (x)/(2) )

If 0 lt alpha lt beta lt gamma lt (pi)/(2) , then the equation (x- sin beta)(x- sin gamma) +(x- sin alpha) (x- sin gamma) + (x- sin alpha) (x-sin beta) = 0 has

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