Step-by-step explanation:
(5cos^{2}60+ 4sec^{2}30- tan^{2}45)/(cosec^{2}30-cot^{2}30)
=
[tex] \frac{5 \times \frac{1}{2} ^{2} + 4 \times { \frac{2}{ \sqrt{3} } }^{2} - {1}^{2} }{ {2}^{2} - { \sqrt{3} }^{2} } \\ = \frac{ \frac{5}{4} + \frac{16}{3} - 1 }{4 - 3} \\ = \frac{15 + 64 - 12}{12} \\ = \frac{67}{12} [/tex]
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Verified answer
Step-by-step explanation:
(5cos^{2}60+ 4sec^{2}30- tan^{2}45)/(cosec^{2}30-cot^{2}30)
=
[tex] \frac{5 \times \frac{1}{2} ^{2} + 4 \times { \frac{2}{ \sqrt{3} } }^{2} - {1}^{2} }{ {2}^{2} - { \sqrt{3} }^{2} } \\ = \frac{ \frac{5}{4} + \frac{16}{3} - 1 }{4 - 3} \\ = \frac{15 + 64 - 12}{12} \\ = \frac{67}{12} [/tex]