Question

Evaluate
Sin30°+tan45°-cosec60°/cot45°+cos60°-sec30π

Answer 1

Answer:

Step-by-step explanation:

given that

\frac{(sin30 + tan45 - cosec60)}{(sec30 + cos60 + cot45)}

\frac{ \frac{1}{2}+1- \frac{2}{ \sqrt{3}}  }{ \frac{2}{ \sqrt{3}}+ \frac{1}{2}+1}  

\frac{ \sqrt{3}+2 \sqrt{3} - 4  }{4 +  \sqrt{3} + 2 \sqrt{3} }  

\frac{ 3 \sqrt{3} - 4  }{4 +  3 \sqrt{3} }  

Rationalise the denominator

\frac{ 3 \sqrt{3} - 4  }{4 +  3 \sqrt{3} } *  \frac{ 3 \sqrt{3} - 4  }{3 \sqrt{3} - 4  }  

\frac{(3 \sqrt{3} - 4 )^2}{ (3 \sqrt{3} )^2-(4)^2 }

\frac{27+16-24 \sqrt{3} }{27-16}

\frac{43-24 \sqrt{3} }{11}