Question

If cos theta =1/2,then cos theta (cos theta - sec theta )

Answer 1

Step-by-step explanation:

Cos @=1/2

sec @=2

Therefore, cos @- sec@ = 1/2-2= -3/2

Answer 2

If cosθ = 1/2 , then cosθ (cosθ - secθ) = - 3/4

Given :

$\displaystyle \sf{cos \: \theta = \frac{1}{2} }$

To find :

$\displaystyle \sf{ cos \: \theta( cos \: \theta -sec \: \theta) }$

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that

$\displaystyle \sf{ cos \: \theta = \frac{1}{2} }$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ cos \: \theta( cos \: \theta -sec \: \theta) }$

$\displaystyle \sf{ = (cos \: \theta \times cos \: \theta) -(cos \: \theta \times sec \: \theta) }$

$\displaystyle \sf{ = {cos}^{2} \: \theta -(cos \: \theta \times \frac{1}{cos \: \theta} ) }$

$\displaystyle \sf{ = {cos}^{2} \: \theta -1 }$

$\displaystyle \sf{ = {\bigg( \frac{1}{2} \bigg)}^{2} - 1}$

$\displaystyle \sf{ = \frac{1}{4} - 1 }$

$\displaystyle \sf{ = \frac{1 - 4}{4} }$

$\displaystyle \sf{ = - \frac{ 3}{4} }$

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