Question

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

Answer 1

sin 30=1/2, tan 45=1, cosec 60=√2, sec 30=2/√3, cos 60=√2, cot 45=1
=1/2+1-√2/2/√3+√2+1

Answer 2

Answer:

${\boxed{\longrightarrow {\bf \dfrac{43-24\sqrt{3}}{11}}}}$

Step-by-step explanation:

$\longrightarrow \bf \dfrac{\sin 30^{\circ}+\tan 45^{\circ}-cosec\;60^{\circ}}{\sec 30^{\circ}+\cos 60^{\circ}+\cot 45^{\circ}}\\ \\ \\ {\underline {\bf Now,\;we\;know\;values\;of\;following\;trignometric\;ratios,}}\\ \\ \\ \longrightarrow \sf \sin 30^{\circ}=\dfrac{1}{2}\\ \\ \\ \longrightarrow \sf \tan 45^{\circ}=1\\ \\ \\ \longrightarrow \sf cosec\;60^{\circ}=\dfrac{2}{\sqrt{3}}\\ \\ \\ \longrightarrow\sf \sec 30^{\circ}=\dfrac{2}{\sqrt{3}}\\ \\ \\ \longrightarrow \sf \cos 60^{\circ}=\dfrac{1}{2}$

$\longrightarrow \sf \cot 45^{\circ}=1\\ \\ \\ {\underline{\bf Now,\;put\;the\;values,}}\\ \\ \\ \longrightarrow \sf \dfrac{\sin 30^{\circ}+\tan 45^{\circ}-cosec\;60^{\circ}}{\sec 30^{\circ}+\cos 60^{\circ}+\cot 45^{\circ}}\\ \\ \\ \longrightarrow \sf \dfrac{\dfrac{1}{2}+1-\dfrac{2}{\sqrt{3}}}{\dfrac{2}{\sqrt{3}}+\dfrac{1}{2}+1}$

$\longrightarrow \sf \dfrac{\dfrac{\sqrt{3}+2\sqrt{3}-4}{2\sqrt{3}}}{\dfrac{4+\sqrt{3}+2\sqrt{3}}{2\sqrt{3}}}\\ \\ \\ \longrightarrow \sf \dfrac{3\sqrt{3}-4}{3\sqrt{3}+4}\\ \\ \\ \longrightarrow \sf \dfrac{3\sqrt{3} -4}{3\sqrt{3}+4}\times \dfrac{3\sqrt{3} -4}{3\sqrt{3} -4}$

$\longrightarrow \sf \dfrac{27-12\sqrt{3}-12\sqrt{3}+16}{(3\sqrt{3})^{2}-4^{2}}\\ \\ \\ \longrightarrow \sf \dfrac{43-24\sqrt{3}}{27-16}\\ \\ \\ {\boxed{\longrightarrow {\bf \dfrac{43-24\sqrt{3}}{11}}}}$

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