Home
Class 11
MATHS
Without using tables, prove that (sin12^...

Without using tables, prove that `(sin12^0)(sin48^0)(sin54^0)=1/8`

Text Solution

Verified by Experts

LHS `=sin12^(@)sin48^(@)sin54^(@)`
`=1/2.(2sin48^(@)sin12^(@)).sin(90^(@)-36^(@))`
`=1/2[cos(48^(@)-12^(@))-cos(48^(@)+12^(@))].cos36^(@)`
`=1/2[cos(48^(@)-12^(@))-cos(48^(@)+12^(@))].cos36^(@)`
`=1/2[cos36^(@)-cos60^(@)].cos36^(@)`
`=1/2[(sqrt(5)+1)/(4)-1/2].((sqrt(5)+1)/(3))`
`=1/2(sqrt(5)+1-2)/(4).(sqrt(5)+1)/(4)`
`=((sqrt(5)-1)(sqrt(5)+1))/(32)`
`=(5-1)/(32)=4/(32)=1/8` = 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 12^0sin 48^0sin 54^0=1/8dot

Prove that: sin20^0sin40^0sin80^0=(sqrt(3))/8

Prove that: sin38^0+sin 22^0=sin 82^0

Prove that sin6^0sin42^0sin66^0sin78^0=1/(16)

Prove that: sin10^0sin30^0sin50^0sin70^0=1/(16)dot

Prove that: sin10^0sin30^0sin50^0sin70^0=1/(16)dot

Prove that: sin10^0sin30^0sin50^0sin70^0=1/(16)dot

Prove that: sin 50^0-sin 70^0+sin 10^0=0

Write the value of sin 12^0sin48^0sin54^0dot

Prove that: sin20^0sin40^0sin60^0sin80^0=3/(16)