prove it - sin12 ×cos78 + cos12 ×sin 78 =1
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Sin(A+B) =SinACosB+cosASinB
Sin90=sin12cos78+cos12sin78
Sin90=sin12cos78+cos12sin78
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sin12° × cos78° + cos12° × sin78°
××××××××××××××××××××××××
We know,
Cos∅ = sin(90 - ∅)
Sin∅ =cos(90 - ∅)
×××××××××××××××××××××××
sin(90 - 78) × cos78° + cos(90 - 78) × sin78
cos78 × cos78 + sin78 × sin78
cos²78 + sin²78
××××××××××××××××
We know,
cos²∅ + sin²∅ = 1
×××××××××××××××××××
cos²78 + sin²78
=> 1
Hence, proved.
I hope this will help you
(-:
××××××××××××××××××××××××
We know,
Cos∅ = sin(90 - ∅)
Sin∅ =cos(90 - ∅)
×××××××××××××××××××××××
sin(90 - 78) × cos78° + cos(90 - 78) × sin78
cos78 × cos78 + sin78 × sin78
cos²78 + sin²78
××××××××××××××××
We know,
cos²∅ + sin²∅ = 1
×××××××××××××××××××
cos²78 + sin²78
=> 1
Hence, proved.
I hope this will help you
(-:
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