` Delta ABC` में सिद्ध कीजिए कि -
` sin^(2) A+ sin^(2) B + sin^(2) C = 2+2 cos A cos B cos C.`

Explanation

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