Home
Class 12
MATHS
If (cos6x+6cos4x+15cos2x+10)/(cos5x+5cos...

If `(cos6x+6cos4x+15cos2x+10)/(cos5x+5cos3x+10cosx)=1`, then find the smallest positive value of x.

Text Solution

Verified by Experts

The correct Answer is:
`x=60^(@)`
`(cos 6x+6cos4x+15cos2x+10)/(cos5x+5cos3x+10cosx)=1`
`rArr((cos 6x+cos 4x)+5(cos4x+cos2x)+10(cos2x+1))/(cos5x+5cos 3x+10cosx)=1`
`rArr (2cos x[cos 5x+5cos 3x+10cosx])/(cos 5x+5cos2x+10cos x)=1`
`rArr cos x=(1)/(2)`
`therefore x=60^(@)`.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.4|26 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.5|6 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.2|7 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

y=(cos6x+6cos4x+15cos2x+10)/(cos5x+5cos3x+10cos x), the n(dy)/(dx)

If y=(cos6x+6cos4x+15cos2x+10)/(cos5x+5cos3x+10cos x) then (dy)/(dx) equals to

The expression (cos6x+6cos4x+15cos2x+10)/(cos5x+5cos3x+10cosx) = lambdacosx , then the value of lambda is ___________.

The expression (cos6x+6cos4x+15cos2x+10)/(cos5x+5cos3x+10cos x) is equal

2cos x-cos3x-cos5x=

1+ cos 2x+ cos4x + cos 6x=

(cos6A+6cos4A+15cos2A+10)/(cos5A+5cos3A+10cos A)=k cos A rArr K=

The expression (cos 6x+6cos 4x+15 cos 2x+10)/(cos 5x+5 cos 3x+10 cos x)

If (cos5x+cos4x)/(2cos3x-1)=cos x+cos nx then find n'

3sin x+5cos x=5 then find the value of 5sin x-3cos x