The number of integral values of k for which the equation sin^−1(x)+tan^−1(x)=2k+1 has a solution is
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We are doing calculations in principal values of inverse trigonometric functions.
Final Answer : There are two values of k for which given equation has solution.
I. e. k=0,-1.
Steps and Understanding :
1) Inverse trigonometric functions are continues and differentuable in their respective domain.
2) We will find range of LHS and RHS expression.
3) Then, we will observe values at which these two approaches same.
RHS will always give odd numbers.
Final Answer : There are two values of k for which given equation has solution.
I. e. k=0,-1.
Steps and Understanding :
1) Inverse trigonometric functions are continues and differentuable in their respective domain.
2) We will find range of LHS and RHS expression.
3) Then, we will observe values at which these two approaches same.
RHS will always give odd numbers.
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