Inverse Trigonometric Functions

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Find the value of tan -1 - Wired Faculty

Question

Find the value of tan^-1 $open square brackets 2 space cos space open parentheses 2 space sin to the power of negative 1 end exponent 1 half close parentheses close square brackets$

Solution

Let space space space space straight y space equals space sin to the power of negative 1 end exponent 1 half space space space space space space where space space minus straight pi over 2 less or equal than straight r less or equal than straight pi over 2 therefore space space space space space space sin space space straight y space equals space 1 half space space space space space space where space space minus straight pi over 2 less or equal than straight r less or equal than straight pi over 2 therefore space space space space space space space straight y space equals straight pi over 6 therefore space space space space space space space tan to the power of negative 1 end exponent open square brackets 2 space cos space open parentheses 2 space sin to the power of negative 1 end exponent space 1 half close parentheses close square brackets equals space tan to the power of negative 1 end exponent space open square brackets 2 space cos space open parentheses 2 cross times straight pi over 6 close parentheses close square brackets space space space space space space space space space space space space tan space to the power of negative 1 end exponent open square brackets 2 space cos straight pi over 3 close square brackets equals tan to the power of negative 1 end exponent open square brackets 2 cross times 1 half close square brackets equals tan to the power of negative 1 end exponent left parenthesis 1 right parenthesis equals straight pi over 4