Math, asked by Bt21army, 10 months ago

express in the product form 1+2 cos 20°​

Answers

Answered by mad210203
2

Given:

Given expression is 1 + 2cos 20°​.

To find:

We need to find the product form of given expression.

Solution:

The given expression is 1 + 2cos 20°​.

We should find the product form.

To find the product form, first we should simplify the given expression.

\Rightarrow  1 + 2cos 20^\circ

\Rightarrow  1 + 2(cos 20^\circ)

The value cos20^\circ=0.93969262078.

So, substitute this value in above expression.

\Rightarrow  1 + 2(0.93969262078)

Multiplying the terms,

\Rightarrow  1 +  1.87938524157

Adding the terms,

\Rightarrow  2.87938524157

\Rightarrow  2.9 (Approximately)

If we multiply any number with 1, it results the same number.

\Rightarrow  2.9\times1\\

\Rightarrow  1\times2.9

Therefore, the product form of given expression is 1\times2.9.

Answered by pulakmath007
5

SOLUTION

TO EXPRESS

In the product form 1 + 2 cos 20°

FORMULA TO BE IMPLEMENTED

We are aware of the Trigonometric formula that

 \displaystyle \sf{ \cos  \alpha  +  \cos  \beta  = 2 \cos  \bigg( \frac{ \alpha  +  \beta }{2}  \bigg)\cos  \bigg( \frac{ \alpha   -   \beta }{2}  \bigg)}

EVALUATION

 \displaystyle \sf{ 1  +  2 \cos   {20}^{ \circ} }

 \displaystyle \sf{ = 2 \bigg(  \frac{1}{2}   +   \cos   {20}^{ \circ} \bigg) }

 \displaystyle \sf{ = 2 \bigg(    \cos   {60}^{ \circ} +   \cos   {20}^{ \circ} \bigg) }

 \displaystyle \sf{   =2 \times  2  \times \cos  \bigg( \frac{  {60}^{ \circ}   +   {20}^{ \circ}  }{2}  \bigg)\cos  \bigg( \frac{  {60}^{ \circ}    -    {20}^{ \circ}  }{2}  \bigg)}

 \displaystyle \sf{   =2 \times  2  \times \cos  \bigg( \frac{  {80}^{ \circ}     }{2}  \bigg)\cos  \bigg( \frac{  {40}^{ \circ}    }{2}  \bigg)}

 \displaystyle \sf{   = 4 \cos  {40}^{ \circ} \cos  {20}^{ \circ} }

FINAL ANSWER

 \displaystyle \sf{ 1  +  2 \cos   {20}^{ \circ} = 4 \cos  {40}^{ \circ} \cos  {20}^{ \circ}}

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