Maths-
General
Easy
Question
If
, then the smallest interval in which θ lies is
The correct answer is: ![0 less or equal than theta less or equal than pi over 4](data:image/png;base64,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)
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell theta equals sin to the power of negative 1 end exponent invisible function application x plus cos to the power of negative 1 end exponent invisible function application x minus tan to the power of negative 1 end exponent invisible function application x equals pi over 2 minus tan to the power of negative 1 end exponent invisible function application x end cell row cell open square brackets because sin to the power of negative 1 end exponent invisible function application x plus cos to the power of negative 1 end exponent invisible function application x equals pi over 2 close square brackets end cell row cell not stretchy rightwards double arrow theta equals cot to the power of negative 1 end exponent invisible function application x end cell end table](data:image/png;base64,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)
Since,
, therefore ![0 less or equal than theta less or equal than pi over 4](data:image/png;base64,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)
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