Question

sin30°+tan45°- cosec60°
$\div$
sec30°+cos60°+cot45°​

Answer 1

GIVEN THAT

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

\frac{ \frac{1}{2}+1- \frac{2}{ \sqrt{3}} }{ \frac{2}{ \sqrt{3}}+ \frac{1}{2}+1}32+21+121+1−32

\frac{ \sqrt{3}+2 \sqrt{3} - 4 }{4 + \sqrt{3} + 2 \sqrt{3} }4+3+233+23−4

\frac{ 3 \sqrt{3} - 4 }{4 + 3 \sqrt{3} }4+3333−4

Rationalise the denominator

\frac{ 3 \sqrt{3} - 4 }{4 + 3 \sqrt{3} } * \frac{ 3 \sqrt{3} - 4 }{3 \sqrt{3} - 4 }4+3333−4∗33−433−4

\frac{(3 \sqrt{3} - 4 )^2}{ (3 \sqrt{3} )^2-(4)^2 }(33)2−(4)2(33−4)2

\frac{27+16-24 \sqrt{3} }{27-16}27−1627+16−243

\frac{43-24 \sqrt{3} }{11}1143−243

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Answer 2

Answer:

sin 30° + tan 45°-cosec 60°/sec 30° + cos 60° + cot 45°

= 1/2+1-2/√3 divide 2\√3+1/2+1

=1/2+1-2√3*√3/2+1/2+1

=1/2+1-1+1/2+1

= 4/2 = 2