Question

2sin5π/12sinπ/12=1/2

Answer 1

Hey !!!

From LHS

2sin5π/12 sinπ/12

=> 2sin(π/2 - π/12 ) ×sinπ/12

=> sin(π/2-π/12) ×sinπ/12

=> 2cosπ/12 ×sinπ/12

•°• 2sinA×cosA= sin2A

like that ..

=> sin 2× 180°/12

=> sin360/12

=> sin30°

=> 1/2 Hence RHS prooved

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Hope it helps you !!!

@Rajukumar111

Answer 2

HELLO DEAR,

we know that:-

2sinx siny = cos (x - y) - cos(x - y).

NOW use the formula here,

2sin5π/12 sinπ/12

=> cos(5π/12 - π/12) - cos(5π/12 + π/12)

=> cos4π/12 - cos6π/12

=> cosπ/3 - cos π/2
[ cosπ/3 = 1/2 , cosπ/2 = 0 ]

=> 1/2 - 0 = 1/2

I HOPE ITS HELP YOU DEAR,
THANKS