The number of real solutions of the equation \sin^{-1}(\sum^{\infty}_{i=1}x^{i+1}-x\sum^{\infty}_{i=1}(x/2)^i)=\pi/2-\cos^{-1}(\sum^{\infty}_{i=1}(-x/2)^i-\sum^{\infty}_{i=1}(-x)^{i}) lying in the interval (-1/2,1/2) is ________. (Here, the inverse trigonometric functions \sin^{-1}x and \cos^{-1}x assume value in [-\pi/2,\pi/2] and [0,\pi] respectively.) [JEE Adv 2018 P1]

Inverse Trigonometric Functions

Section: Mathematics

Question : 8 of 14

Marks: +1, -0

The number of real solutions of the equation

sin−1(

∞

∑

i=1

xi+1−x‌

∞

∑

i=1

(

)i)=

−cos−1(

∞

∑

i=1

(−

)i−

∞

∑

i=1

(−x)i)

lying in the interval (−

) is ________.
(Here, the inverse trigonometric functions sin−1x and cos−1x assume value in [−

] and [0,π] respectively.)

[JEE Adv 2018 P1]

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