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Inverse Trigonometric Functions

Short Answer Type

41.

Prove the following :

$3 space sin to the power of negative 1 end exponent straight x equals sin to the power of negative 1 end exponent left parenthesis 3 straight x minus 4 straight x cubed right parenthesis comma space straight x element of open square brackets negative 1 half comma 1 half close square brackets$

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42.

Prove the following :

$3 space cos to the power of negative 1 end exponent straight x equals cos to the power of negative 1 end exponent thin space left parenthesis 4 straight x cubed minus 3 straight x right parenthesis comma space straight x element of open square brackets 1 half comma space 1 close square brackets$

143 Views

43.

Prove space that space fraction numerator 9 straight pi over denominator 8 end fraction minus 9 over 4 space sin to the power of negative 1 end exponent 1 third equals 9 over 4 sin to the power of negative 1 end exponent fraction numerator 2 square root of 2 over denominator 3 end fraction.

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44.
Show that $tan to the power of negative 1 end exponent 1 half plus tan to the power of negative 1 end exponent 2 over 11 equals tan to the power of negative 1 end exponent 3 over 4.$

tan to the power of negative 1 end exponent 1 half plus tan to the power of negative 1 end exponent 2 over 11 equals tan to the power of negative 1 end exponent open square brackets fraction numerator begin display style 1 half plus 2 over 11 end style over denominator 1 minus begin display style 1 half end style cross times begin display style 2 over 11 end style end fraction close square brackets equals tan to the power of negative 1 end exponent open square brackets fraction numerator begin display style fraction numerator 11 plus 4 over denominator 22 end fraction end style over denominator begin display style fraction numerator 22 minus 2 over denominator 22 end fraction end style end fraction close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space tan to the power of negative 1 end exponent open parentheses 15 over 20 close parentheses equals space tan to the power of negative 1 end exponent open parentheses 3 over 4 close parentheses space rightwards double arrow space straight R. straight H. straight S. therefore space space space space straight L. straight H. straight S. space equals space straight R. straight H. straight S

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45.

Prove that $sin to the power of negative 1 end exponent space straight x plus space cos to the power of negative 1 end exponent space straight x equals straight pi over 2$

170 Views

46.

Prove that $tan to the power of negative 1 end exponent straight x plus cot to the power of negative 1 end exponent straight x equals straight pi over 2 comma space straight x element of straight R$

116 Views

47.

Prove that $cos e c to the power of negative 1 end exponent x plus s e c to the power of negative 1 end exponent x equals straight pi over 2 comma space open vertical bar x close vertical bar greater or equal than 1$