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1- cosa+cosb-cos(a+b)/1+cosa-cosb-cos(a+b) = tan a/2cotb/2. Prove it

1- cosa+cosb-cos(a+b)/1+cosa-cosb-cos(a+b) = tan a/2cotb/2. Prove it

Grade:11

1 Answers

Vikas TU
14149 Points
5 years ago
Write numerator of L.HS as:
= > (1-cosA)(1+cosA) + sinAsinB
= > 4sinA/2cosB/2(sinA/2cosB/2 + cosA/2sinB/2)
=> 4sinA/2cosB/2sin((A+B)/2)..................(1)
 
then write denominotor too by adjustmnet,
we get
deno.
as
=>  4cosA/2siinB/2sin((A+B)/2)
 
Divide them and get the R.H.S .i.e. tan a/2cotb/2..

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