Prove that 4(Cos60°+Sin84) - V3 + V5
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Answer:
Given, 4(cos66
o
+sin84
o
)
=4(cos(30
o
+36
o
)+sin(30
o
+54
o
))
=4(cos30cos36−sin30sin36+sin30cos54+sin54cos30)
=4(
2
3
cos36−
2
1
sin36+
2
1
cos54+sin54×
2
3
)
=4(
2
3
cos(90−54)−
2
1
sin36+
2
1
cos(90−36)+
2
3
sin64
o
)
=4(
2
3
sin54
o
−
2
1
sin36
o
+
2
1
sin36
o
+
2
3
sin54
o
)
=8
2
3
sin54
o
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