prove the following
iv ) sin18ºcos39° + sin6° cos15º = sin24° cos33°
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Answer:
use complement concept
Step-by-step explanation:
LHS=sin18
∘
cos39
∘
+sin6
∘
cos15
∘
=
2
1
[2sin18
∘
cos39
∘
+2sin6
∘
cos15
∘
]
We know that 2sinAcosB=sin(A+B)+sin(A−B)
=
2
1
[sin(18
∘
+39
∘
)+sin(18
∘
−39
∘
)+sin(6
∘
+15
∘
)+sin(6
∘
−15
∘
)]
=
2
1
[sin47
∘
−sin21
∘
+sin21
∘
−sin9
∘
]
=
2
1
[sin47
∘
−sin9
∘
]
=
2
1
×2cos(
2
47+9
)sin(
2
47−9
)
=cos(
2
56
)sin(
2
38
)
=cos28
∘
sin19
∘
Hence LHS
=RHS
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