Question

Cot 30 upon sec 30 cosec 30 upon tan 45 - 2 cos 0 upon sin 30 cos square 45

Answer 1

$Value \: of \:\left(\frac{cot30\degree}{sec30\degree}\right) \times \left(\frac{cosec 30\degree}{tan 45\degree}\right) - 2 \left(\frac{cos 0\degree}{sin 30\degree}\right) \times cos^{2} 45\degree$

$= \left(\frac{\frac{cos 30\degree}{sin 30 \degree}}{\frac{1}{cos 30\degree}}\right) \times \left(\frac{\frac{1}{sin30\degree}}{tan 45\degree}\right) - 2 \left(\frac{cos 0\degree}{sin 30\degree}\right) \times cos^{2} 45\degree$

$= \frac{cos^{2} 30 \degree }{sin 30\degree}\times \frac{1}{sin 30\degree \times tan 45\degree } - 2 \left(\frac{cos 0\degree}{sin 30\degree}\right) \times cos^{2} 45\degree$

$= \frac{cos^{2} 30\degree}{sin^{2} 30 \degree \times tan 45\degree } - 2 \left(\frac{cos 0\degree}{sin 30\degree}\right) \times cos^{2} 45\degree$

$= \frac{cot^{2} 30 \degree}{tan 45\degree } -2 \left(\frac{cos 0\degree}{sin 30\degree}\right) \times cos^{2} 45\degree$

$= \frac{ (\sqrt{3})^{2}}{1} - 2 \times \frac{1}{\frac{1}{2}} \times \left(\frac{1}{\sqrt{2}}\right)^{2}$

$= 3 - 2 \times \frac{2}{1} \times \frac{1}{2}$

$= 3 - 2 \\= 1$

Therefore.,

$\red{Value \: of \:\left(\frac{cot30\degree}{sec30\degree}\right) \times \left(\frac{cosec 30\degree}{tan 45\degree}\right) - 2 \left(\frac{cos 0\degree}{sin 30\degree}\right) \times cos^{2} 45\degree}$

$\green {= 1}$

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