Home
Class 11
MATHS
Prove that:(sinx+sin3x)/(cosx+cos3x)=tan...

Prove that:`(sinx+sin3x)/(cosx+cos3x)=tan2x`

Text Solution

Verified by Experts

`cosA+cosB = 2cos((A+B)/2)cos((A-B)/2)`
`sinA+sinB = 2sin((A+B)/2)cos((A-B)/2)`
`L.H.S = (sinx+sin3x)/(cosx+cos3x)`
Using the above formulas for `cosA+cosB` and `sinA+sinB`
`=(2sin2xcosx)/(2cos2xcosx) = (sin2x)/(cos2x)=tan2x=R.H.S.`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    NCERT|Exercise MISCELLANEOUS EXERCISE|10 Videos

  • TRIGONOMETRIC FUNCTIONS

    NCERT|Exercise EXERCISE 3.1|7 Videos

  • TRIGONOMETRIC FUNCTIONS

    NCERT|Exercise EXERCISE 3.4|9 Videos

  • STRAIGHT LINES

    NCERT|Exercise EXERCISE 10.5|2 Videos

Similar Questions

Explore conceptually related problems

Prove that :(sin x+sin3x)/(cos x+cos3x)=tan2x

Prove that: (sin5x+sin3x)/(cos5x+cos3x)=tan4x

(sin5x+sin3x)/(cos5x+cos3x)=tan4x

Prove that: ,,(sin5x+sin3x)/(cos5x+cos3x)=tan4x

Prove : (sin 7x +sin 3x)/(cos 7x+cos 3x) = tan 5x

Prove that: (sin5x-2sin3x+sinx)/(cos5x-cos x)=tanx

Prove (sin5x-2sin3x+sin x)/(cos5x-cos x)=tan x

Prove that: (sin3x+sin x)sin x+(cos3x-cos x)cos x=0

Prove that (sin5x-2sin3x+sin x)/(cos5x-cos x)=tan x