Question

solve for x where 0° less than or equal to X less than equal to 90° sin square x Plus cos square 30 degrees equal to 5 by 4​

Answer 1

Answer:

x = 45°

Step-by-step explanation:

given,

sin²x + cos²30°=5/4

we know that cos30°=√3/2

so the eq becomes,

sin²x + (√3/2)² = 5/4

sin²x + ¾ = 5/4

sin²x =5/4-3/4

sin²x = ½

so, sinx =1/√2

so for this condition to be satisfied,

x= 45° ( since, 0°<x<90°)

Answer 2

$x=45^{\circ}$

Step-by-step explanation:

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

Where $0^{\circ}\leq x\leq 90^{\circ}$

We know that

$cos30^{\circ}=\frac{\sqrt 3}{2}$

Substitute the value

$sin^2x+(\frac{\sqrt3 }{2})^2=\frac{5}{4}$

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

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

$sin^2x=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}$

$sinx=\pm \frac{1}{\sqrt 2}$

$sinx=-\frac{1}{\sqrt 2}$

It is not possible because $0\leq x\leq 90$

$sinx=\frac{1}{\sqrt 2}$

$sinx=sin45^{\circ}$

Using $sin45^{\circ}=\frac{1}{\sqrt 2 }$

$x=45^{\circ}$

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https://brainly.in/question/2379834:Answered by Ananyaaishwarya