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

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

Text Solution

AI Generated Solution

To prove that \( \sin(-420^\circ) \cos(390^\circ) + \cos(-660^\circ) \sin(330^\circ) = -1 \), we will simplify the left-hand side step by step. ### Step 1: Simplify \( \sin(-420^\circ) \) Using the property of sine, \( \sin(-\theta) = -\sin(\theta) \): \[ \sin(-420^\circ) = -\sin(420^\circ) \] Now, we can simplify \( 420^\circ \): ...
Promotional Banner

Topper's Solved these Questions

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise EXERCISES 3A|11 Videos

  • TRIGNOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise EXERCISES 3B|22 Videos

  • STRAIGHT LINES

    NAGEEN PRAKASHAN|Exercise Exercise|206 Videos

Similar Questions

Explore conceptually related problems

Prove that: sin420^(@)cos390^(@)+cos(-300^(@))sin(-330^(@))=1

Prove that: "sin"420^(@) cos390^(@)+cos(-660^(@))"sin"(-390^(@))=(1)/(2) .

sin120^(@)cos150^(@)-cos240^(@)sin330^(@)=

sin120^(@)cos150^(@)-cos240^(@)sin330^(@)

Prove that: sin600^(@)cos390^(@)+cos480^(@)s in150^(@)=-1

Prove that: sin780^(@)s in120^(@)+cos240^(@)sin390^(@)=(1)/(2)

sin150^(@).cos120^(@)+cos330^(@)*sin660^(@)=-1

Prove that (sin32^(@)cos58^(@)+cos32^(@)sin58^(@))=1.

Prove that: (cos40^(@)+cos50^(@))/(sin40^(@)+sin50^(@))=1

Prove that (sin20^(@) + sin40^(@)) + (cos20^(@) + cos40^(@))=(sqrt(3)+1)cos10^(@)