`-1/(4 sqrt2)`
`1/8`
`-1/(2 sqrt2)`
`1/(2 sqrt2)`
`2`
`1`
`1/2`
`1/3`
`-6`
`-5`
`1`
`0`
Only `1`
Only `2`
Both `1` and `2`
Neither `1` nor `2`
`-4`
`-3`
`3`
`2`
` (1 + cos x) /( (x + sin x) ( 1 - sin x) )`
` (1 - cos x) /( (x + sin x) ( 1 + sin x) )`
` (1 - cos x) /( (x - sin x) ( 1 + cos x) )`
` (1 + cos x) /( (x - sin x) ( 1 - cos x) )`
` -1/2`
`2`
`sin x + cos x`
`sin x - cos x`
`0`
`1/2`
`1`
`x`
`tan theta `
`cot theta `
`sin 2 theta `
`cos 2 theta`
`sec^2 theta`
`- cosec^2 theta`
`(sec^3 theta)/(a theta)`
None of these
`3x^2`
`(3x)/2`
`x`
`3/2`
`y/x`
`-y/x`
`x/y`
`-x/y`
`10`
`2`
`1`
`0`
` a/b`
` b/a `
`1`
`0`
`0`
`1`
`1/x`
`x`
`-1`
`0`
`1`
`2`
`0`
`-1`
`1/2`
`1`
`- (log_5 x)^(-2)`
`(log_5 x)^(-2)`
`- (log_x 5)^(2)`
`(log_x 5)^(-2)`
`e^(-1)`
`e`
`1`
`0`
`x`
`x log_e 10`
`- ( (log_x 10)^2 (log_(10) e) )/x`
`x log_(10) e`
`cos^(-1) x + cos^(-1) sqrt (1-x^2)`
`1/(cos x) +1/(cos sqrt (1-x^2) )`
`pi/2`
`0`
`-1`
`1`
`2`
`4`
-1
1
2
4
`5/3`
`3/5`
`- 5/3`
`- 3/5`
` -1`
`1/3`
`1/2`
`1`
`5/2`
`5`
`1/5`
`1/(10)`
`1 + e`
`1 - e`
`1 + 2e`
None of these
`-1`
`0`
`1`
`2`
`cos(cosx)`
`cos(sinx)`
`cos(sinx)cosx`
`cos (cosx) cosx`
`-1`
`0`
`1`
Does not exist
`x^2/(2y)`
`x/(2y)`
`x^2/y`
None of these
`0`
`1`
`-1`
`2`
`1`
`2`
`2 sec x tan x`
`2 sec^2 x tan x`
`0`
`1`
`2`
None of these
Only I
Only II
Both I and II
Neither I nor II
`2^(sin x) ln 2`
`(sin x) 2^(sin x -1)`
`(cos x) 2^(sin x-1)`
none of the above
`-1`
`0`
`1`
`2`
`xy`
`x/y`
`-y/x`
`-x/y`
`xy`
`x/y`
`-y/x`
`-x/y`
`1/5`
`1/10``
`1/20`
None of these
`1/5`
`1/10`
`1/20`
None of these
`-2/(x-1)`
`-2/(x-1)^2`
`2/(x-1)^2`
`2/(x-1)`
`-2/(x-1)`
`-2/(x-1)^2`
`2/(x-1)^2`
`2/(x-1)`
`1`
`-1`
`x`
`x^(1/2)`
`2^x (log 2)^2`
`x(x-1) 2^(x-2)`
`2^(x+1) (log 2)`
`2^x (log_(10) 2)^2`
`tan^2 x`
`cot^2 x`
`-1`
`1`
`5`
`4`
`2`
`-1`
`0`
`sin (2t)`
`-cos (2t)`
`-1/2`
`0`
`1`
`1/x`
`x`