Home
Class 11
MATHS
Prove that: sin5A=5sinA-20sin^(3)A+16s...

Prove that:
`sin5A=5sinA-20sin^(3)A+16sin^(5)A`

Text Solution

Verified by Experts

LHS `=sin5A=sin(3A+2A)`
`=(3sinA-4sin^(3)A)(1-2sin^(2)A)+(4cos^(3)A-3cosA)2sinAcosA`
`=(3sinA-4sin^(3)A)(1-2sin^(2)A)+(4cos^(2)A-3)2sinAcos^(2)A`
`=(3sinA-4sin^(3)A)(1-2sin^(2)A)+[4(1-sin^(2)A)-3]2sina(1-sin^(2)A`
`=(3sinA-4sin^(3)A)(1-2sin^(2)A)+(2sinA-2sin^(3)A)(1-4sin^(2)A)`
`=3sinA-6sin^(3)A-4sin^(3)A+8sin^(5)A +2sinA-8sin^(3)A-2sin^(3)A+8sin^(5)A`
`5sinA-20sin^(3)A+16sin^(5)A` = 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

If A=30^(@) , then prove that : sin3A=3sinA-4sin^(3)A

Prove that: sinA.sin(60^(@)+A).sin(60^(@)-A)=1/4sin3A

sin5A=5cos^4AsinA-10cos^2Asin^3A+sin^5A

prove that : (sinA+2sin3A+sin5A)/(sin3A+2sin5A+sin7A)=(sin3A)/(sin5A)

Prove that: sin(pi/5)sin( (2pi)/5)sin(3pi/5)sin(4pi/5)=5/(16)

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

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

Prove that: i) sin20^(@)sin40^(@)sin60^(@)sin80^(@)=3/16 ii) sin10^(@)sin50^(@)sin60^(@)sin70^(@)=sqrt(3)/16 iii) sin20^(@)sin40^(@)sin80^(@)=sqrt(3)/8

Prove that: (sin5A-sin7A+sin8A-sin4A)/(cos4A+cos7A-cos5A-cos8A)=cot 6A

Prove that: (sin(A-C)+2sinA+sin(A+C))/(sin(B-C)+2sinB+sin(B+C))=(sinA)/(sinB)