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Prove that: t a n 720^0-cos 270^0-sin 15...

Prove that: `t a n 720^0-cos 270^0-sin 150^0cos 120^0=1/4`

Text Solution

Verified by Experts

(a) `tan720^@-cos270^@-sin150^@cos120^@`
`=0-0-(sin30^@)(-cos60^@)=1/2xx1/2=1/4`
(b) `sin780^@sin480^@+cos120^@sin150^@`
`=sin(720^@+60^@)sin(360^@+120^@)`
`+cos(180^@-60^@)sin(180^@-30^@)`
`=sin(60^@)sin(120^@)-cos(60^@)sin(30^@)`
`sqrt3/2xxsqrt3/2-1/2xx1/2=3/4-1/4=1/2`
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