the value of
is
Answers
Answer:
√5 / 2
Step-by-step explanation:
Given---> Sin( π/10 ) + Sin( 3π/10 )
To find---> Value of given expression
Solution--->
Sin( π / 10 ) + Sin ( 3π / 10 )
= Sin ( 3π / 10 ) + Sin ( π / 10 )
We know that,
SinC + SinD = 2 Sin ( C + D / 2 ) Cos ( C - D / 2 ) applying it here
= 2 Sin{ ( 3π/10 + π/10) / 2} Cos { (3π/10 - π/10)/2}
= 2 Sin{( 4π /10) / 2} Cos{( 2π/10)/2}
= 2 Sin( 4π / 20 ) Cos ( 2π / 20 )
= 2 Sin ( π / 5 ) Cos ( π / 10 )
= 2 Sin ( 36° ) Cos (18° )
Putting value of Sin36° and Cos18° ,
= 2 {√(10 - 2√5 ) / 4 } { √(10 + 2√5 ) /4 }
= ( 2/ 16 ) √{ ( 10 - 2√5 ) ( 10 + 2√5 ) }
Applying a² - b² = ( a + b ) ( a - b ) , we get,
= ( 1/8) √{ ( 10 )² - ( 2√5 )² }
= ( 1 / 8 ) √( 100 - 4× 5 )
= √(100 - 20 ) / 8
= √80 / 8
= √(16 × 5) / 8
= 4 √5 / 8
= √5 / 2
- √5/2
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