Question

if tan theta = 1/√3 then find the value 4cos²theta-3/3sin²theta+1​

Answer 1

Answer:

0

Step-by-step explanation:

tan theta=p/b=1/root 3

h²=p²+b²

h²=(1)²+(root 3)²

h²=1+3

h²=4

h=2

Cos theta=b/h=root 3/2

Sin theta=p/h=1/2

4 cos²theta-3/3sin²theta+1

=4(root 3/2)²-3/3(1/2)²+1

=4(3/4)-3/3(1/4)+1

=3-3/3/4+1

=0/3+4/4

=0/7/4

=0/7×4

=0/7

=0

Answer 2

Answer:

(10$\sqrt{3\\}$ - 6)/5

Step-by-step explanation:

tan theta = 1/ $\sqrt{3\\}$

tan theta = tan 30                    [tan 30 = 1/$\sqrt{3}$]

theta = 30

⇒ 4 cos²theta - 3/ 3sin²theta + 1

= 4 cos²30 - 3/ 3sin²30 + 1

= 4 * $\sqrt{3}$/2 - 3/3*1/2 + 1                                 [sin 30 = $\sqrt{3}$/2; cos 30 = 1/2]

= 2$\sqrt{3}$ - 3/ 5/2

= 2$\sqrt{3}$ - 6/5

= (10$\sqrt{3}$ - 6)/5

HOPEFULLY YOU UNDERSTOOD :)