Question

find the value of tan²π/3 + 4 cosπ/4 + 3 sec²π/6 + 5cos²π/2 (1mark)​

Answer 1

Given ,

$\tt{tan}^{2} \frac{\pi}{3} + 4cos \frac{\pi}{4} + 3 {sec}^{2} \frac{\pi}{6} + 5 {cos}^{2} \frac{\pi}{2}$

We know that ,

• π/3 = 60°
• π/4 = 45°
• π/6 = 30°
• π/2 = 90

Thus ,

$\tt \implies {tan}^{2} 60+ 4cos45+ 3 {sec}^{2} 30 + 5 {cos}^{2} 90$

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

$\tt \implies 3 + 2 + 2 + 0$

$\tt \implies 7$

Therefore , the required value is 7

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