Evaluate the following:frac{5 cos ^{2} 60^{ci | vedclass

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Question

(A) Given expression: $\frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-	an ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}}$Using trig

Vedclass · Accepted Answer

$67$

Vedclass · Answer

(A) Given expression: $\frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-	an ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}}$Using trigonometric values: $\cos 60^{\circ} = 1/2$,$\sec 30^{\circ} = 2/\sqrt{3}$,$	an 45^{\circ} = 1$,$\sin 30^{\circ} = 1/2$,$\cos 30^{\circ} = \sqrt{3}/2$.Substituting these values:$= \frac{5(1/2)^{2} + 4(2/\sqrt{3})^{2} - (1)^{2}}{(1/2)^{2} + (\sqrt{3}/2)^{2}}$$= \frac{5(1/4) + 4(4/3) - 1}{1/4 + 3/4}$$= \frac{5/4 + 16/3 - 1}{4/4}$$= \frac{(15 + 64 - 12)/12}{1}$$= 67/12$

Evaluate the following:
$\frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-\tan ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}}$ (in $/12$)

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Evaluate the following:$\frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-\tan ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}}$ (in $/12$)