Math, asked by AbhiramiGNath, 1 year ago

Prove that

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

Answers

Answered by siddhartharao77
66
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!

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Answered by tardymanchester
16

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

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