Evaluate each of the following tan2-60o-4cos2-45o-3sec2-30o-5-cos2-90o-cosec-30o-sec60o-cot2-30o

Tan^2 60^o+4cos^2 45^o+3sec^2 30^o+5 cos^2 90^o/cosec 30^o+sec60^o cot^2 30^o =tan^2 60^o+4cos^2 45^o+3/cos^2 30^o+5 cos^2 90^o/1/sin 30^o+1/cos 60^o 1/tan^2 30 ...

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Standard X

Mathematics

Standard Values of Trigonometric Ratios

Evaluate each...

Question

Evaluate each of the following

$\frac{t a n^{2} 60^{o} + 4 c o s^{2} 45^{o} + 3 s e c^{2} 30^{o} + 5 c o s^{2} 90^{o}}{c o s e c 30^{o} + s e c 60^{o} - c o t^{2} 30^{o}}$

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Solution

$\frac{t a n^{2} 60^{o} + 4 c o s^{2} 45^{o} + 3 s e c^{2} 30^{o} + 5 c o s^{2} 90^{o}}{c o s e c 30^{o} + s e c 60^{o} - c o t^{2} 30^{o}}$

$= \frac{t a n^{2} 60^{o} + 4 c o s^{2} 45^{o} + \frac{3}{c o s^{2} 30^{o}} + 5 c o s^{2} 90^{o}}{\frac{1}{s i n 30^{o}} + \frac{1}{c o s 60^{o}} - \frac{1}{t a n^{2} 30^{o}}}$

$= \frac{(\sqrt{3})^{2} + 4 \times {(\frac{1}{\sqrt{2}})}^{2} + \frac{3}{{(\frac{\sqrt{3}}{2})}^{2}} + 5 \times 0}{\frac{1}{(\frac{1}{2})} + \frac{1}{(\frac{1}{2})} - \frac{1}{{(\frac{1}{\sqrt{3}})}^{2}}}$

$= \frac{3 + 2 + 4}{2 + 2 - 3} = 9$

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Similar questions

Q. Evaluate each of the following :

\frac{{tan}^{2} 60^{\circ} + 4 {cos}^{2} 45^{\circ} + 3 {sec}^{2} 30^{\circ} + 5 {cos}^{2} 90^{\circ}}{cosec 30^{\circ} + sec 60^{\circ} - {cot}^{2} 30^{\circ}}

Q. Evaluate

\frac{{tan}^{2} 60^{\circ} + 4 {cos}^{2} 45^{\circ} + 3 {sec}^{2} 30^{\circ} + 5 {cos}^{2} 90^{\circ}}{c o s e c 30^{\circ} + sec 60^{\circ} - {cot}^{2} 30^{\circ}}

Q. Evaluate each of the following

\frac{\tan^{2} 60 ° + 4 \cos^{2} 45 ° + 3 \sec^{2} 30 ° + 5 \cos^{2} 90 °}{cosec 30 ° + \sec 60 ° - \cot^{2} 30 °}

\frac{(\tan^{2} 60 ° + 4 \sin^{2} 45 ° + 3 \sec^{2} 30 ° + 5 \cos^{2} 90 °)}{(cosec 30 ° + \sec 60 ° - \cot^{2} 30 °)} = ?

(a)

\frac{9}{7}

(b) 9
(c)

\frac{7}{9}

(d) 6

Q. Evaluate:

(i) s i n^{2} 30^{\circ} . c o s^{2} 45^{\circ} + 4 t a n^{2} 30^{\circ} + \frac{1}{2} s i n^{2} 90^{\circ} + \frac{1}{8} c o t^{2} 60^{\circ}

(i i) \frac{t a n^{2} 60^{\circ} + 4 s i n^{2} 45^{\circ} + 3 s e c^{2} 30^{\circ} + 5 c o s^{2} 90^{\circ}}{c o s e c 30^{\circ} + s e c 60^{\circ} - c o t^{2} 30^{\circ}}

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Evaluate each of the following tan2 60o+4cos2 45o+3sec2 30o+5 cos2 90ocosec 30o+sec60o−cot2 30o

tan2 60o+4cos2 45o+3sec2 30o+5 cos2 90ocosec 30o+sec60o−cot2 30o =tan2 60o+4cos2 45o+3cos2 30o+5 cos2 90o1sin 30o+1cos60o−1tan2 30o =(√3)2+4×(1√2)2+3(√32)2+5×01(12)+1(12)−1(1√3)2 =3+2+42+2−3=9

Evaluate each of the following

$\frac{t a n^{2} 60^{o} + 4 c o s^{2} 45^{o} + 3 s e c^{2} 30^{o} + 5 c o s^{2} 90^{o}}{c o s e c 30^{o} + s e c 60^{o} - c o t^{2} 30^{o}}$