If k=\tan (\frac{\pi}{4}+\frac{1}{2} \cos ^{-1} (\frac{2}{3}) ) +\tan (\frac{1}{2} \sin ^{-1} (\frac{2}{3}) ), then the number of solutions of the equation \sin ^{-1}(k x-1)= \sin ^{-1} x-\cos ^{-1} x is \_\_\_\_ . [28 Jan 2026 Shift 1]

Inverse Trigonometric Functions

Section: Mathematics

Question : 2 of 95

Marks: +1, -0

If k=tan(‌

+‌

cos−1(‌

))+tan(‌

sin‌−1(‌

)), then the number of solutions of the equation sin‌−1(kx−1)=sin‌−1x−cos−1x is ____ .

[28 Jan 2026 Shift 1]

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