Question Number 18474 by Tinkutara last updated on 22/Jul/17
$$\boldsymbol{\mathrm{Assertion}}-\boldsymbol{\mathrm{Reason}}\:\boldsymbol{\mathrm{Type}}\:\boldsymbol{\mathrm{Question}} \\ $$$$\mathrm{STATEMENT}-\mathrm{1}\::\:{f}\left({x}\right)\:=\:\mathrm{log}_{\mathrm{cos}{x}} \mathrm{sin}{x}\:\mathrm{is} \\ $$$$\mathrm{well}\:\mathrm{defined}\:\mathrm{in}\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right). \\ $$$$\boldsymbol{\mathrm{and}} \\ $$$$\mathrm{STATEMENT}-\mathrm{2}\::\:\mathrm{sin}{x}\:\mathrm{and}\:\mathrm{cos}{x}\:\mathrm{are} \\ $$$$\mathrm{positive}\:\mathrm{in}\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right). \\ $$
Answered by sushmitak last updated on 22/Jul/17
$$\mathrm{1}\:\mathrm{true} \\ $$$$\mathrm{2}\:\mathrm{true} \\ $$$$\mathrm{2}\:\mathrm{is}\:\mathrm{correct}\:\mathrm{explaination}\:\mathrm{for}\:\mathrm{1}. \\ $$
Commented by Tinkutara last updated on 22/Jul/17
$$\mathrm{But}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{both}\:\mathrm{are}\:\mathrm{true}\:\mathrm{but}\:\mathrm{2}\:\mathrm{is}\:\mathrm{not} \\ $$$$\mathrm{explanation}\:\mathrm{of}\:\mathrm{1}. \\ $$
Commented by sushmitak last updated on 23/Jul/17
$$\mathrm{log}_{{x}} {y}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{for}\:{x}>\mathrm{0}\:\mathrm{and}\:{x}\neq\mathrm{1} \\ $$$$\mathrm{and}\:{y}>\mathrm{0}. \\ $$
Commented by Tinkutara last updated on 23/Jul/17
$$\mathrm{Thanks}\:\mathrm{Sir}! \\ $$