Home
Class 11
MATHS
Prove that sin6^0sin42^0sin66^0sin78^0-1...

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

Text Solution

Verified by Experts

LHS `=sin6^(@)sin42^(@)sin66^(@)sin78^(@)`
`=1/4(2sin66^(@)sin6^(@)).(2sin78^(@)sin42^(@))`
`=1/4[cos(66^(@)-6^(@))-cos(66^(@)+6^(@))] [cos(78^(@)-42^(@))-cos(78^(@)+42^(@))]`
`=1/4[cos60^(@)-cos72^(@)][cos36^(@)-cos120^(@)]`
`=1/4[1/2-cos(90^(@)-18^(@))][cos36^(@)-cos(90^(@)+30^(@))]`
`=1/4[1/2-sin18^(@)][cos36^(@)+sin30^(@)]`
`=1/4[1/2-(sqrt(5)-1)/(4)][(sqrt(5)+1)/(4)+1/2]`
`=1/4[(2-sqrt(5)+1)/(4)][(sqrt(5)+1+2)/(4)]`
`=3-sqrt(5)(3+sqrt(5))/(64)=(9-5)/(64)`
`=4/64=1/16`= 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: sin6^0sin42^0sin 66^0sin 78^0=1/(16)

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

Prove that: sin20^0sin40^0sin60^0sin80^0=3/(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: sin6^(@)sin42^(@)sin66^(@)sin78^(@)=1/16

Prove that: tan6^0tan42^0tan66^0tan78^0=1.

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

Prove that: \ sin 10^0sin 50^0sin 60^0sin 70^0=(sqrt(3))/(16)