Question

sin105°sin75° =rude 3 +2/4​

Answer 1

Solution :

i )sin105

= sin( 90 + 15 )

= cos15 ---( 1 )

ii )sin75

= sin( 90 - 15 )

= cos 15----( 2 )

iii ) cos15

= cos( 45 - 30 )

= cos45cos30+sin45sin30

= (1/√2)(√3/2)+(1/√2)(1/2)

= (√3+1)/(2√2)----( 3 )

Now ,

LHS = sin105sin75

= cos15cos15

= cos²15

= [ (√3+1)/2√2]²

= (√3+1)²/8

= -[(√3)²+1+2√3]/8

= [4+2√3]/8

= [2(2+√3)]/8

= (2+√3)/4

= RHS

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