Question

Find the value of
4tansquare45-cosec²30 + cos²30.please say in brief it's urgent ​

Answer 1

Answer:

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Answer 2

To find:-

Value of :

$\bigstar \sf 4 \: {tan}^{2} 45 \degree - {cosec}^{2} \: 30 \degree - {cos}^{2} \: 30 \degree$

Solution:-

$\bigstar \sf 4 \: {tan}^{2} 45 \degree - {cosec}^{2} \: 30 \degree - {cos}^{2} \: 30 \degree$

tan 45° = 1

cosec 30° = 2

cos 30° = √3/2

$\implies \sf 4 \times {(1)}^{2} - {(2)}^{2} - { \dfrac{ (\sqrt{3} )}{2} }^{2}$

$\implies \sf 4 \times 1 - 4 - \dfrac{3}{4}$

$\implies \sf \cancel{4} - \cancel{ 4} - \dfrac{ 3 }{4}$

$\implies \sf - \dfrac{3}{4}$

Therefore,

$\sf 4 \: {tan}^{2} 45 \degree - {cosec}^{2} \: 30 \degree - {cos}^{2} \: 30 \degree = - \dfrac{3}{4}$