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as , 3π/2 = 3 × 180° / 2 = 270°
2π = 2 × 180° = 360°
cos ( 270° + x ) = sin x
cos ( 360° + x ) = cos x
cot ( 270° - x ) = tan x
cot ( 360° + x ) = cot x
now ,
LHS = sin x • cos x { cot x + tan x }
=> sin x cos x { (sin x / cos x) + ( cos x / sin x ) }
=> taking LCM ,
=> sin x cos x { sin ² x + cos ² x } / sin x cos x
=> sin x cos x will cancel each other out !
=> sin ² x + cos ² x = 1 = RHS
Proved !
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