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Find sin16 using sin(AB)=sinAcosBcosAsinB ?

Answer
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Hint: As we know that the above question is related to trigonometry as sine, cosine are the trigonometric ratios. The given trigonometric identity is a basic difference formula of the trigonometric ratio. In the above question we will break down the degree in two different numbers and then apply the given trigonometric identity.

Complete step by step solution:
As per the given question we have sin16 .
It can be written as sin16=sin(9074) .Here we have A=90 and B=74 .
So we can write it as sin(9074)=sin90cos74cos90sin74 .
We know the value of sin90=1 and cos90=0 . The value of cos74 is the same in degrees and radians. To obtain the value of 74 in radian, we multiply 74 by π180=3790×π .
Therefore the value is 0.275639(approx) .
By putting the values in the formula we have sin16=1×0.275630×sin74 .
Hence the required value of sin16 is 0.27563 .
So, the correct answer is “ 0.27563 ”.

Note: Before solving this kind of question we should have the clear concept of trigonometric ratios, identities and their formulas. We should note that in the above solution sin(9074) can also be written as cos74 , as the identity says that sin(90θ)=cosθ . It gives us the same value as in the above solution. WE should know all the identities as there are several ways to solve a question.