Question

If Tan^2 45° -cos^2 30°=>x sin45°cos45°,then find x​

Answer 1

Answer:

L. H. S = tan^2 45° - cos^2 30° = 1 - (root {3}/2)^2

=> 1 - 3 /4

=> 1/4

R. H. S = x ( 1/root {2})(1/root{2})

= x ( 1/2)

Given, 1/4 = x/2

x = 1/2

Answer 2

SOLUTION:-

Given,

$tan {}^{2} 45 \degree - cos {}^{2} 30 \degree = xsin45 \degree \: cos45 \degree$

The value of:

tan45°= 1

cos30°= √3/2

sin45°= 1/√2

cos45°=1/√2

So,

$= > (1) {}^{2} - ( \frac{ \sqrt{3} }{2} ) {}^{2} = x( \frac{1}{ \sqrt{2} }) \times ( \frac{1}{ \sqrt{2} } ) \\ \\ = > 1 - \frac{3}{4} = \frac{x}{2} \\ \\ = > \frac{4 - 3}{4} = \frac{x}{2} \\ \\ = > \frac{1}{4} = \frac{x}{2} \\ \\ = > 4x = 2 \: \: \: \: \: [cross \: \: multiplication] \\ \\ = > x = \frac{2}{4} \\ \\ = > x = \frac{1}{2}$

hope it helps ☺️