Question

Prove that

tan720° - cos 270°- sin 150°cos 120° = 1/4

Answer 1

Tan 720 = Tan(360 + 360)

               = Tan 360

               = 0.


cos 270 = cos(180 + 90)

               = -cos90

               = 0.



sin150 = sin(90 + 60)

            = cos 60

            = 1/2.



cos 120 = cos(180 - 60)

              = -cos 60

              = -1/2.


Now,

Tan 720 - cos 270 - sin 150 * cos 120

$= 0 - 0 -( \frac{1}{2} ) (- \frac{1}{2})$

$= 0 + 0 + \frac{1}{4}$

$\frac{1}{4}$


Hope this helps!

Answer 2

Answer:

RHS=LHS proof below.

Step-by-step explanation:

Given : $\tan 720^\circ-\cos 270^\circ-\sin 150^\circ\cos 120^\circ=\frac{1}{4}$

To find : Prove that the given expression is equal?

Solution :

We know,

$\tan 720^\circ=\tan (360+360)$

$\tan 720^\circ=\tan 360^\circ$

$\tan 720^\circ=0$

$\cos 270^\circ=\cos (180+90)$

$\cos 270^\circ=-\cos 90^\circ$

$\cos 270^\circ=0$

                       

$\sin 150^\circ=\cos (90+60)$

$\sin 150^\circ=-\cos 60^\circ$

$\sin 150^\circ=\frac{1}{2}$

$\cos 120^\circ=\cos (180-60)$

$\cos 120^\circ=-\cos 60^\circ$

$\cos 120^\circ=-\frac{1}{2}$

Substitute all the values in the given expression LHS,

$RHS=\tan 720^\circ-\cos 270^\circ-\sin 150^\circ\cos 120^\circ$

$RHS=0-0-(\frac{1}{2})(-\frac{1}{2})$

$RHS=\frac{1}{4}$

$RHS=LHS$