Question

5 cos 0 - 2 sin 30° 3 cos 30° +3 ein 29 secsi
tan 30 x teen 60 x cos60​

Answer 1

The question is wrong the correct question is mentioned below

     5Cos0°- (2Sin30°×3Cos30°)+(3Sin29°×Tan30°×Tan60°×Cos60°)

Given :

  5Cos0°- (2Sin30°×3Cos30°)+(3Sin29°×Tan30°×Tan60°×Cos60°)

To Find :

The value of the equation

Solution :

• The equation can be solved by substituting the values of trigonometric functions
• By substituting the values in the given equation we get

        5Cos0°- (2Sin30°×3Cos30°)+(3Sin29°×Tan30°×Tan60°×Cos60°)

           $=(5\times1)-(2\times\frac{1}{2} \times3 \times\frac{\sqrt{3}}{2})+(3 \times0.48 \times\frac{1}{\sqrt{3} } \times\sqrt{3} \times \frac{1}{2})$

           $=5-(3\times\frac{\sqrt{3} }{2})+3 \times \frac{\sqrt{3} }{4}$

           $=5-(3\times\frac{\sqrt{3} }{4} )$

           = 5 -1.3

           = 3.7

  The value of the equation is 3.7

   

Answer 2

Given:

$\frac{(5\cos0 - 2\sin30 + \sqrt{3}\cos30)}{(\tan30\times \tan60 \times \cos60 + 3\sin29 \sec61)} = \frac{11}{7}$

To find:

proving

Solution:

The given question has several mistakes so, the correct question can be described as follows:

Question:

$\frac{(5\cos0 - 2\sin30 + \sqrt{3}\cos30)}{(\tan30\times \tan60 \times \cos60 + 3\sin29 \sec61)} = \frac{11}{7}$

values:

$\Rightarrow \cos 0 = 1\\ \Rightarrow\sin 30 = \frac{1}{2}\\ \Rightarrow \cos 30 = \frac{\sqrt{3}}{2}\\ \Rightarrow \cos 60 = \frac{1}{2}\\ \Rightarrow \tan 30 = \frac{1}{\sqrt{3}}\\ \Rightarrow \tan 60 = \sqrt{3}$

solve L.H.S part:

$\Rightarrow \frac{(5\cos0 - 2\sin30 + \sqrt{3}\cos30)}{(\tan30\times \tan60 \times \cos60 + 3\sin29 \sec61)} = \frac{(5\times 1 - 2\frac{1}{2} + \sqrt{3}\frac{\sqrt{3}}{2})}{(\frac{1}{\sqrt{3}}\times \sqrt{3} \times \frac{1}{2} + 3\sin29 \frac{1}{\cos 61})}$

                                                     $= \frac{(5\times 1 - 2\frac{1}{2} + \sqrt{3}\frac{\sqrt{3}}{2})}{(\frac{1}{\sqrt{3}}\times \sqrt{3} \times \frac{1}{2} + 3\sin29 \frac{1}{\cos(90-29)})} \\\\=\frac{(5\times 1 - 2\frac{1}{2} + \sqrt{3}\frac{\sqrt{3}}{2})}{(\frac{1}{\sqrt{3}}\times \sqrt{3} \times \frac{1}{2} + 3 \frac{\sin29}{\sin29})}$

                                                     $=\frac{(5 - 1 +\frac{{3}}{2})}{(\frac{1}{2} + 3)} \\\\=\frac{\frac{{10-2+3}}{2}}{\frac{1+6}{2}} \\\\=\frac{\frac{{11}}{2}}{\frac{7}{2}} \\\\=\frac{11}{7}$

L.H.S = R.H.S