Question

if tan theta =1/root 3 then cos 2 theta =​

Answer 1

Answer:

1/2

Step-by-step explanation:

Cos 2tgeta= Cos^2theta– Sin^2theta

so tan theta is 1/root 3

cos theta will be root 3/2

and sin theta will be 1/2

putting in formula

3/4 - 1/4

1/2

Answer 2

Answer:

The value is

$cos2θ = \frac{1}{2}$

Step-by-step explanation:

Given that,

$tanθ = \frac{1}{ \sqrt{3} }$

We know that the value of tanθ is

$tanθ = \frac{opposide \: side}{adjacent \: side} = \frac{1}{ \sqrt{3} }$

Therefore,the length of opposite side is 1 unit and length of Adjacent side is \sqrt{3} units.

Now length of hypotenuse is given as

$= \sqrt{1 {}^{2} + ( \sqrt{3}) {}^{2} } = 2 \: units$

Now we find the value of cosθ as follows

$cosθ = \frac{adjacent}{hypotenuse} = \frac{ \sqrt{3} }{2}$

Therefore,Cos2θ can be found by relation

$cos2θ = 2cos {}^{2} θ - 1 = 2( \frac{ \sqrt{3} }{2} ) {}^{2} - 1 \\ = \frac{1}{2}$

Therefore,the value of cos2θ is

$cos2θ = \frac{1}{2}$

#SPJ3