Question

Sin^2 x + cos^2 30 = 5/4,
Solve for x


Best answer will be marked as brainliest

Answer 1

Answer:

Step-by-step explanation:

x + root 3/2 x root 3/2 = 5/4

x + 3/4 = 5/4

x = 5/4 - 3/4

x = 2/4 = 1/2

Answer 2

Question :-

$\bf \: { \sin}^{2} x + { \cos}^{2}30 = \frac{5}{4} \\ \bf \: find \: the \: value \: of \: x$

Answer :-

$\longmapsto \bf \: \: x = \pm \: 45$

Solution :-

We have ,

$\longrightarrow \: \bf { \sin}^{2} x + { \cos}^{2} 30 = \frac{5}{4} \\ \\ \longrightarrow \bf \: { \sin}^{2} x + {( \cos 30)}^{2} = \frac{5}{4} \\ \because \: \cos 30 = \frac{ \sqrt{3} }{2} \\ \\ \longrightarrow \bf \: { \sin}^{2} x + { \bigg(\frac{ \sqrt{3} }{2} \bigg)}^{2} = \frac{5}{4} \\ \\ \longrightarrow \bf \: { \sin}^{2} x + \frac{3}{4} = \frac{5}{4} \\ \\ \: \longrightarrow \bf \: { \sin}^{2} x = \frac{5}{4} - \frac{3}{4} \\ \\ \longrightarrow \bf \: { \sin}^{2} x = \frac{ 5 - 3}{4} \\ \\ \longrightarrow \bf \: { \sin}^{2} x = \frac{2}{4} \\ \\ \longrightarrow \bf { \sin}^{2} x = \frac{1}{2} \\ \\ \sf \: taking \: \: \sqrt{} \: on \: both \: sides \\ \\ \longrightarrow \bf \sqrt{ {( \sin x)}^{2} } = \pm \frac{1}{ \sqrt{2} } \\ \: \\ \longrightarrow \bf \: \sin x = \pm \: \sin 45 \\ \\ \bf \: \: hence \: \: \boxed{ \bf \: x = \pm 45 \: \: } \:$

Verification :-

$\star \bf \: \: if \: x = + 45 \\ \\ \to \bf { \sin}^{2} 45 + { \cos}^{2} 30 = \frac{5}{4} \\ \\ \to \bf \: \frac{1}{2} + \frac{3}{4} = \frac{5}{4} \\ \\ \to \bf \: \frac{5}{4} = \frac{5}{4} \\ \\ \star \bf\: if \: x = - 45 \\ \\ \to \bf \: { \sin}^{2} ( - 45) + { \cos}^{2} 30 = \frac{5}{4} \\ \\ \to \: \frac{1}{2} + \frac{3}{4} = \frac{5}{4} \\ \\ \to \bf \: \frac{5}{4} = \frac{5}{4}$

Hence verified .