If `tan^(-1)(sin^2theta-2sintheta+3)+cot^(-1)(5^sec^(2y)+1)=pi/2,`then value of `cos^2theta-sintheta`is equal to0 (b) `-1`(c) `1`(d) none of these

If `tan^(-1)(sin^2theta-2sintheta+3)+cot^(-1)(5^sec^(2y)+1)=pi/2,`then

1.	If `tan^(-1)(sin^2theta-2sintheta+3)+cot^(-1)(5^sec^(2y)+1)=pi/2,`then value of `cos^2theta-sintheta`is equal to0 (b) `-1`(c) `1`(d) none of these
Answer» Correct Answer - C From the given equation `sin^(2) theta - 2 sin theta + 3 = 5^("sec"^(2)y) + 1`, we get `(sin theta -1)^(2) + 2 = 5^("sec^(2)y) + 1` `L.H.S. le 6, R.H.S. ge 6` Possible solution is `sin theta = -1` when L.H.S. = R.HgtS. `rArr cos^(2) theta = 0` `rArr cos^(2) theta - sin theta = 1`

`tan^(-1)[(cosx)/(1+sinx)]`is equal to`pi/4-x/2,forx in (-pi/2,(3pi)/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-(3pi)/2,pi/2)`
The value of `sin^(-1)(sin12)+sin^(-1)(cos12)=`
Find the principal value of `sin^(-1)(-1/sqrt2)-2tan^(-1)(-sqrt3)+cos^(-1)(-1/2)`.
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If `x , y , z in [-1,1]`such that `sin^(-1)x+sin^(-1)y+sin^(-1)z=-(3pi)/2,`find the value of `x^2+y^2+z^2dot`A. 1B. 3C. `(3pi^(23))/(4)`D. `3pi^(2)`
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The value of `cos^(-1)(cos(5pi)/3)+sin^(-1)(sin(5pi)/3)`is`pi/2`(b) `(5pi)/3`(c) `(10pi)/3`(d) 0
Find the principal value of `sin^(-1)(-1/sqrt2)+tan^(-1)(-1/sqrt3)+sec^(-1)(2)`