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Inverse Trigonometric Functions

Question
CBSEENMA12035691
Wired Faculty App

If space tan to the power of negative 1 end exponent straight x plus tan to the power of negative 1 end exponent straight y space equals space straight pi over 4 comma space xy less than 1 comma space then space write space the space value space of space straight x plus straight y plus xy.

Solution

Given that tan to the power of negative 1 end exponent straight x plus tan to the power of negative 1 end exponent straight y space equals straight pi over 4 space and space xy less than 1.
We need to find the value of x+y+xy.
tan to the power of negative 1 end exponent straight x plus tan to the power of negative 1 end exponent straight y space equals space straight pi over 4
rightwards double arrow space tan to the power of negative 1 end exponent open parentheses fraction numerator straight x plus straight y over denominator 1 minus xy end fraction close parentheses space equals space straight pi over 4 space open square brackets because space xy less than 1 close square brackets rightwards double arrow space tan open square brackets tan to the power of negative 1 end exponent open parentheses fraction numerator straight x plus straight y over denominator 1 minus xy end fraction close parentheses close square brackets space equals space tan open parentheses straight pi over 4 close parentheses rightwards double arrow space space fraction numerator straight x plus straight y over denominator 1 minus xy end fraction equals 1 rightwards double arrow straight x plus straight y space equals space 1 minus xy rightwards double arrow space straight x plus straight y plus xy equals space space 1

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