किसी `Delta ABC` में सिध्द कीजिये कि:
`(a) cos 2A + cos 2B + cos 2C =-1- 4 cos A cos B cos C`
`( b) cos 2A + cos 2B-cos 2C=1 -4 sin A sin B cos C`

Explanation

`L.H.S= cos 2A + cos 2 B - cos 2C`
` = 2cos (A+B) cos (A -B) - (2 cos^(2) C-1)`
` = 2 cos (180^(@) - C) cos ( A - B) -2`
` = cos^(2) C+1 ( :' A + B+ C = 180^(@))`
` = 1 - 2 cos C* cos (A- B) - 2 cos^(2) C`
` = 1 -2 cos C [ cos (A- B) + cos C] `
` = 1 - 2 cos C [ cos (A-B) + cos { 180^(@)-`
` (A+B)}]`
` = 1-2 cos C [ cos (A-B) -cos (A+B)]`
` = 1-2 cos C* 2 sin A sin B`
` = 1-4 sin A sin B cos C = R.H.S`