Question

4. If root 3 tan theta = 1 and theta is an acute angle, find the value of sin 30 + cos 20​

Answer 1

Required Answer:-

Given:

• √3 tan(x) = 1 and 0°⩽x⩽90°.

To find:

• sin(3x) + cos(2x)

Answer:

• sin(3x) + cos(2x) = 1.5

Solution:

Given,

√3 tan(x) = 1

➡ tan(x) = 1/√3

From Trigonometry Ratio Table,

➡ tan(x) = tan(30°)

➡ x = 30°

Hence,

sin(3x) + cos(2x)

= sin(3 × 30°) + cos(2 × 30°)

= sin(90°) + cos(60°)

Now, look at the table. From table, we get,

sin(90°) = 1 and cos(60°) =1/2, thus,

= 1 + 1/2

= 3/2

= 1.5

Hence,

➡ sin(3x) + cos(2x) = 1.5

Learn More:

• Trigonometry Ratio Table: It is a table that helps us to find out the trigonometric ratios of standard angles. It consists of six Trigonometric Functions namely sine, cosine, tangent, cotangent, cosecant and secant.
• For example:- In this question, we have found the values of sin(90°) and cos(60°) from the Trigonometry Ratio Table.

T-Ratio Table:

$\sf \blue{ Trigonometric \: Values} \\ \boxed{\begin{array}{c|c|c|c|c|c} \sf \underline{Angle} & 0^{\circ} & 30^{\circ} & 45^{\circ} & 60^{\circ} & 90^{\circ} \\ \sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1 \\ \cos \theta & 1 & \dfrac{\sqrt{3}}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{1}{2} & 0 \\ \tan\theta & 0 & \dfrac{1}{\sqrt{3}} & 1 & \sqrt{3} & \textsf{Not D{e}fined}\end{array}}$

Answer 2

Answer:

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