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tan^-1(2)+tan^-1(3)=cosec^-1(X) solve. Hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

tan^-1(2)+tan^-1(3)=cosec^-1(X) solve.   Hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Grade:11

2 Answers

Aditya Gupta
2081 Points
4 years ago
note that tan^-1(2) is greater than tan^-1(1)= pi/4
similarly tan^-1(3) is greater than tan^-1(1)= pi/4
so, the sum tan^-1(2)+tan^-1(3) is greater than pi/4 + pi/4 = pi/2
however, range of RHS cosec^-1(X) is [-pi/2, 0)U(0,pi/2].
so, LHS is greater than pi/2 but RHS is less than pi/2
so, there exists no solution.
kindly approve :)
Arun
25750 Points
4 years ago
 
Dear student
 
tan^-1 (2) + tan^-1 (3) = pi +  tan^-1 (5/-5) = pi – pi/4 = 3pi/4
 
hence cosec^-1(x) = 3pi/4
hence no solution as cosec^-1 x has range from [- pi/2,0) U (0, pi/2]
 
 

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