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find the value of sin48.cos78=? a.√5+1/8 b.1+√5/8 c.1-√5/8 d.√5-1/8 the question is correct please give solution of this question..please

find the value of sin48.cos78=?
a.√5+1/8
b.1+√5/8
c.1-√5/8
d.√5-1/8
the question is correct please give solution of this question..please

Grade:11

1 Answers

kkbisht
90 Points
5 years ago
Correct answer is option no (d)
 Solution: sin48. cos78=sin48.cos(90-12) 
Now using only  Cos(A-B)  Trigonometric-formula we have 
sin48( cos90. cos12+ sin90.sin12)= sin48.(0.cos12 + 1.sin12)=sin48.sin12
Now multiply and divide by 2 the last expression= 1/2(2 sin48 sin12)= 1/2(cos(48-12) + cos(48+12))=1/2(cos36-cos60)
=1/2{(root5 +1)/4-1/2) = 1/2{(root5+1)-2)/4= 1/8(root5 -1)
 
 as  sinB= Cos(A-B) - Cos(A+B))
by : kkbisht
 

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