The number of solutions of the equation sin − 1 ( c a x ) + sin − 1 ( c b x ) = sin − 1 x where a 2 + b 2 = c 2 , a , b , c are positive real numbers, is (are)

Question

The number of solutions of the equation sin − 1 ( c a x ​ ) + sin − 1 ( c b x ​ ) = sin − 1 x where a 2 + b 2 = c 2 , a , b , c are positive real numbers, is (are)

TestHub · Accepted Answer

sin − 1 c a x ​ = sin − 1 x − sin − 1 ( c b x ​ ) ⇒ c a x ​ = x − c 2 b 2 x 2 ​ ​ − 1 − x 2 ​ ( c b x ​ ) ⇒ x = 0 or a = c 2 − b 2 x 2 ​ − b 1 − x 2 ​ x = 0 or 1 − x 2 ​ = 0

Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

Doubts & Discussion

JEE Main + Advanced (1 year 12th class)