Home
Class 11
MATHS
Prove that (cosalpha+cosbeta)^2+(sinalph...

Prove that `(cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2=4cos^2((alpha-beta)/2)dot`

Text Solution

Verified by Experts

Given,`(cos alpha + cos beta)^2 + (sin alpha + sin beta)^2 = cos2alpha + cos2beta + 2 cos alpha cos beta + sin^2alpha + sin^2beta + 2 sin alpha sin beta`
= `(cos^2alpha + sin^2alpha) + (cos^2beta + cos^2beta) + 2(cos alpha cos beta + sin alpha sin beta)`
=` 1 + 1 + 2 cos(alpha – beta)`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that (cos alpha+cos beta)^(2)+(sin(alpha)+sin beta)^(2)=4cos^(2)((alpha-beta)/(2))

Prove that : (cos alpha+cos beta)^(2)+(sin alpha+sin beta)^(2)=4cos^(2)((alpha-beta)/(2))

Prove that: (cos alpha+cos beta)^(2)+(s in alpha+s in beta)^(2)=4cos^(2)((alpha-beta)/(2))

Prove that: (cos alpha+cos beta)^(2)+(s in alpha+s in beta)^(2)=4cos^(2)((alpha-beta)/(2))

Prove that 2sin^(2)beta+4cos(alpha+beta)sin alpha sin beta+cos2(alpha+beta)=cos2 alpha

Prove that cos alpha+cos beta+cos gamma+cos(alpha+beta+gamma)=4cos((alpha+beta)/(2))cos((beta+gamma)/(2))cos((gamma+alpha)/(2))

Prove that cos alpha+cos beta+cos gamma+cos(alpha+beta+gamma)=4cos((alpha+beta)/(2))cos((beta+gamma)/(2))cos((gamma+alpha)/(2))

For all value of alpha,beta,gamma prove that ,cosalpha+cosbeta+cosgamma+cos(alpha+beta+gamma)=4cos(alpha+beta)/2*cos(beta+gamma)/2*cos(gamma+alpha)/2

Prove that |[cos alpha cos beta, cos alpha sin beta , sin alpha],[-sinbeta,cosbeta,0],[sinalpha cosbeta, sinalpha sinbeta, cos alpha]|=cos2alpha

If cosalpha+cosbeta=0=sinalpha+sinbeta , then cos2alpha+cos2beta=?