Question

Solve for x; where 0° ≤ x ≤ 90°

sin² x + cos² 30 = 5/4

Answer 1

The value of ∠x = 45°

Explanation:

We have,

 $\sin^2 x+\cos^230 =\dfrac{5}{4}$ , 0° ≤ x ≤ 90°

To find, the value of ∠x = ?

∴$\sin^2 x+\cos^230 =\dfrac{5}{4}$

⇒  $\sin^2 x+(\dfrac{\sqrt{3}}{2})^2=\dfrac{5}{4}$

Using the trigonometric identity,

$\cos 30=\dfrac{\sqrt{3}}{2}$

⇒  $\sin^2 x+\dfrac{3}{4} =\dfrac{5}{4}$

⇒  $\sin^2 x=\dfrac{5}{4}-\dfrac{3}{4}$

⇒  $\sin^2 x=\dfrac{5-3}{4}=\dfrac{2}{4}$

⇒  $\sin^2 x=\dfrac{1}{2}$

⇒  $\sin x=(+-)\sqrt{\dfrac{1}{2}}$

⇒  $\sin x=\dfrac{1}{\sqrt{2}}$

( Since, first quadrant only positive values)

⇒  $\sin x=\sin 45$

∴ ∠x = 45°

Thus, the value of ∠x = 45°  

Answer 2

Answer:

here is your answer.

hope it will help you,

Thank you,

have a nice day!