જો $y = \tan^{-1} \left( \frac{4x}{1 + 5x^2} \right) + \tan^{-1} \left( \frac{2 + 3x}{3 - 2x} \right)$ હોય,તો $\frac{dy}{dx} = $

$\cos \left[\sin ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)\right]=$

$\cot ^{-1}\left(\frac{1}{2}\right)+\cot ^{-1}\left(\frac{1}{3}\right)=$ . . . . . . .

$\sin \left(\cos ^{-1}\left(-\frac{1}{3}\right)-\sin ^{-1}\left(\frac{1}{3}\right)\right)$ નું મૂલ્ય શું છે?

$x=\frac{1}{5}$ હોય ત્યારે $\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right)$ ની કિંમત શોધો,જ્યાં $0 \leq \cos ^{-1} x \leq \pi$ અને $-\frac{\pi}{2} \leq \sin ^{-1} x \leq \frac{\pi}{2}$ છે.

જો $\operatorname{Tan}^{-1}\left[\frac{1}{1+1(2)}\right]+\operatorname{Tan}^{-1}\left[\frac{1}{1+(2)(3)}\right]+\operatorname{Tan}^{-1}\left[\frac{1}{1+(3)(4)}\right]+\cdots+\operatorname{Tan}^{-1}\left[\frac{1}{1+n(n+1)}\right]=\operatorname{Tan}^{-1} \theta$ હોય,તો $\theta=$