Home
Class 12
MATHS
Prove that: sin10^0sin30^0sin50^0sin70^0...

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

Text Solution

Verified by Experts

`cos 10^(@)cos30^(@)cos50^(@)cos70^(@)`
`=cos 30^(@)cos 10^(@)cos(60^(@)-10^(@))cos(60^(@)+10^(@))`
`=(1)/(4)cos30^(@)cos(3xx10^(@))=(3)/(16)`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.7|5 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.8|9 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.5|6 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

Prove that (cos10^0+sin10^0)/(cos10^0-sin 10^0)=tan55^0

Prove that: cos18^0-sin 18^0=sqrt(2)sin27^0

Prove that sin 20^(@) sin 40^(@) sin 60^(@) sin 80^(@)=3/(16) .

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

Prove that in a A B C ,sin^2A+sin^2B+sin^2C<=9/4dot

The value of sin 10^(@) sin 30^(@) sin 50^(@) sin 70^(@) is equal to .

Prove that 2sin2^0+4sin4^0+6"sin"6^0+.......+180sin180^0=90cot1^0dot

Prove that sin 10° + sin 20° + sin 40° + sin 50°=sin 70° + sin 80

The value of expression (2(sin1^0+sin2^0+sin3^0+...+sin89^0))/(2(cos1^0+cos2^0++cos44^0)+1) (a) sqrt(2) (b) 1/(sqrt(2)) (c) 1/2 (d) 0

Prove that sin 50^(@)-sin 70^(@)+cos 80^(@)=0 .