Home
Class 11
MATHS
Prove that: sin(-420^0)(cos390^0)+cos(-6...

Prove that: `sin(-420^0)(cos390^0)+cos(-660^0)(sin330^0)=-1.`

Text Solution

Verified by Experts

LHS `=sin(-420^(@))cos390^(@) + cos(-660^(@))sin330^(@)`
`-sin420^(@)cos390^(@)+cos660^(@)sin330^(@)`
`=-sin(360^(@)+60^(@))cos(360^(@)+30^(@))+cos(360^(@)+300^(@))sin(360^(@)+30^(@))`
`=-sin60^(@)cos30^(@)+cos300^(@)(-sin30^(@))`
`=-sqrt(3)/2 xx sqrt(3)/2-1/2cos(360^(@))-60^(@)`
`=-3/4-1/2 cos60^(@)`
`=-3/4 -1/2 xx 1/2`
`-3/4 -1/4 =-1`
=RHS Hence proved.
Promotional Banner

Topper's Solved these Questions

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISES 3A|12 Videos

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise EXERCISES 3B|24 Videos

  • STRAIGHT LINES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise|207 Videos

Similar Questions

Explore conceptually related problems

Prove that: sin(-420^0)(cos390^0)+cos(-660^0)(s in330^0)=-1.

Prove that sin(-420^0)(c0s390^0)+cos(-660^0)(sin330^0)=-1

Prove that: sin 80^0-cos 70^0=cos 50^0

Prove that: sin600^0cos 390^0+cos 480^0sin 150^0=-1

Prove that: sin 40^0+sin 20^0=cos 10^0

Prove that: sin 47^0+cos 77^0=cos 17^0

Prove that: sin 23^0+sin 37^0=cos7^0

Prove that: sin(60^0-theta)cos(30^0+theta)+cos(60^0-theta)sin(30^0+theta)=1.

Prove that: cos20^0cos40^0cos60^0cos80^0=1/(16)

Prove that : sin 51^0+cos 81^0=cos 21^0