Question

sin square x + cos square 30 =5÷4.Find value of x if x<0<90​

Answer 1

Answer:

Sin^2x°+cos^2 30°=5/4

Sin^2x°+{(root3)/2}^2=5/4

Sin^2x°+3/4=5/4

Sin^2x°=5/4-3/4

Sin^2x°=2/4

Sin^2x°=1/2

Sinx°=root(1/2)

Sinx°=1/root2

Sinx°=sin45°[sin45=1/root2]

x°=45°

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Answer 2

The value of ∠ x is equal to 45°.

Step-by-step explanation:

We have,

$\sin^2 x+\cos^2 30 =\dfrac{5}{4}$

To find, the value of ∠ x = ?

∴ $\sin^2 x+\cos^2 30 =\dfrac{5}{4}$

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

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

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

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

⇒ $\sin^2 x=\dfrac{1}{2}$

⇒ $\sin^2 x=(\dfrac{1}{\sqrt{2} })^2$

⇒ $\sin^2 x=\sin^2 45$

⇒ ∠ x  = 45°

∴ The value of ∠ x = 45°

Thus, the value of ∠ x is equal to 45°.