Question

sin²x + cos^2 30 = 5/4
Find value of x if 0

Answer 1

Answer:

sin2x + cos2 30 =5/4

sin2x +(-/3/2) =5/4

sin2x + 3/4=5/4

sin2x =2/4

sin2x=1/2

sin x=1/-/2

sin x=sin45

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 = ?

∴ $\sin^2 x+\cos^2 30 =\dfrac{5}{4}$

[ ∵ $\cos 30=\dfrac{\sqrt{3}}{2}$]

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

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

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

⇒ $\sin^2 x=\dfrac{5-3}{4}$

⇒ $\sin^2 x=\dfrac{2}{4}=\dfrac{1}{2}$

⇒ $\sin^2 x=(\dfrac{1}{\sqrt{2}})^2$

[ ∵ $\sin 45=\dfrac{1}{\sqrt{2}}$]

⇒ $\sin^2 x=\sin^2 45$

⇒ x = 45°

Thus, the value of x is equal to 45°.