If ^245^ - ^230^ =x 45^ 45^ then x=? - Vidyadip

MCQ

If $\tan^245^\circ-\cos^230^\circ=\text{x}\sin45^\circ\cos45^\circ$ then $\text{x}=?$

A
$2$
B
$-2$
✓
$\frac{1}{2}$
D
$\frac{-1}{2}$

✓

Answer

Correct option: C.

$\frac{1}{2}$

$\tan^245^\circ-\cos^230^\circ$
$=\text{x}\sin45^\circ\cos45^\circ$
$\Rightarrow(1)^2-\Big(\frac{\sqrt3}{2}\Big)^2$
$=\text{x}\times\frac{1}{\sqrt2}\times\frac{1}{\sqrt2}$
$\Rightarrow1-\frac{3}{4}=\text{x}\times\frac{1}{2}$
$\Rightarrow\frac{1}{4}=\frac{\text{x}}2{}$
$\Rightarrow\text{x}=\frac{1}{2}$

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