Question

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44bca0d166735ae8693a2aeeb5450ebf.docx

Answer 1

Answer:

please send questions , docx file is not opening

Answer 2

SoluTion :-

Expression

$\sf \frac{cos\,58^{\circ}}{sin\,32^{\circ}}+\frac{sin\,22^{\circ}}{cos\,68^{\circ}}-\frac{cos\,38^{\circ}\:\:cosec\,52^{\circ}}{tab\,18^{\circ}\:\:tan\,25^{\circ}\:tan\,60^{\circ}\:tan\,72^{\circ}\:tan\,65^{\circ}}}$

Using Complimentary angles to simplify,

$\sf {sin\,x=cos(90-x)\:\:,\:\:cos\,x=sin(90-x)\:\: and\:\:tan\,x=cot(90-x)}$

Now,

$\sf {\frac{cos\,58^{\circ}}{cos\,(90-32)^{\circ}}+\frac{sin\,22^{\circ}}{sin\,(90-68)^{\circ}}-\frac{cos\,38^{\circ}\times\frac{1}{sin\,52^{\circ}}}{tab\,18^{\circ}\:\:tan\,25^{\circ}\:tan\,60^{\circ}\:cot\,(90-72)^{\circ}\:cot\,(90-65)^{\circ}}}$

$\sf {\Rightarrow \frac{cos\,58^{\circ}}{cos\,58^{\circ}}+\frac{sin\,22^{\circ}}{sin\,22^{\circ}}-\frac{cos\,38^{\circ}\times\frac{1}{cos\,(90-52)^{\circ}}}{tab\,18^{\circ}\:\:tan\,25^{\circ}\:tan\,60^{\circ}\:cot\,18^{\circ}\:cot\,25^{\circ}}}$

$\sf {\Rightarrow 1+1-\frac{cos\,38^{\circ}\times\frac{1}{cos\,38^{\circ}}}{tab\,18^{\circ}\:\:tan\,25^{\circ}\:tan\,60^{\circ}\:\times\frac{1}{tan\,18^{\circ}}\times\frac{1}{tan\,25^{\circ}}}}$

$\sf {\Rightarrow 1+1-\frac{1}{1\times\:tan\,60^{\circ}\:\times1}}}$

$\sf {\Rightarrow 1+1-\frac{1}{tan\,60^{\circ}}}}$

$\sf {\Rightarrow 2-\frac{1}{\sqrt{3}}\ ( \because tan\,60^{\circ}=\sqrt{3} )}$

Value of Given Expression :-

$\sf {\implies \frac{2\sqrt{3}-1}{\sqrt{3}}}$