 # prove that 1-cosA+cosB-cos(A+B)/1+cosA-cosB-cos(A+B)=tanA/2cotB/2

11 years ago

hi veda

take the numerator of L.H.S

1-cosA+cosB-cos(A+B) simplifying 1-cosA = 2sin2  A/2 by half angle identity

cosB-cos(A+B) = 2sin(A/2)sin((A+2B)/2)  difference into product identity

2sin2  A/2 + 2sin(A/2)sin((A+2B)/2)  by simple trigonometric identities

by further simplifying

2sin(A/2)(sin A/2 + sin((A+2B)/2)

now applying sum to product identity

2sin(A/2)(2sin((A+B)/2)cosB/2-------------1

and then take denominator

1+cosA-cosB-cos(A+B)

similarly by half angle and sum into product identity we get

2cos2  A/2 + 2cos(A/2)cos((A+2B)/2)

by further simplifying

2cos(A/2)(cos A/2 - cos((A+2B)/2)

applying difference to product identity we get

2cos(A/2)(2sin((A+B)/2)sinB/2---------------2

now dividing 1 by 2

we get

 tanA/2cotB/2

so proved

We are all IITians and here to help you in your IIT JEE preparation.

Now you can win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

jitender