Question

Please answer 11 question?

Class - 10th
Chapter - Trigonometry

Please be kind and help me ​

Answer 1

Answer:30°

Step-by-step explanation:

We have,

✓3sinx-cosx=0

that is, ✓3sinx=cosx

so, sinx/cosx=1/✓3

we know that , sinx/cosx=tanx

so, tanx=1/✓3

we know that , tan30°=1/✓3

so , x=30°

Answer 2

Required Answer:-

Given:

• √3 sin(x) - cos(x) = 0.
• 0° < x < 90°

To find:

• The value of x.

Solution:

Given that,

➡ √3 sin(x) - cos(x) = 0

➡ √3 sin(x) = cos(x)

➡ √3 = cos(x)/sin(x)

➡ sin(x)/cos(x) = 1/√3

➡ tan(x) = 1/√3

From Trigonometry Ratio Table,

➡ tan(x) = tan(30°)

➡ x = 30°

Hence, the value of x is 30°

Verification:

Let us verify our result.

Taking LHS,

√3 sin(x) - cos(x)

= √3 sin(30°) - cos(30°)

= √3 × 1/2 - √3/2

= √3/2 - √3/2

= 0

Taking RHS,

= 0

Hence, LHS = RHS (Verified)

Trigonometry Ratio Table:

$\sf Trigonometric \: Values \\\ \boxed{\begin{array}{c|c|c|c|c|c} \sf Angle & 0^{\circ} & 30^{\circ} & 45^{\circ} & 60^{\circ} & 90^{\circ} \\ \sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1 \\ \cos \theta & 1 & \dfrac{\sqrt{3}}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{1}{2} & 0 \\ \tan\theta & 0 & \dfrac{1}{\sqrt{3}} & 1 & \sqrt{3} & \infty \end{array}}$