Q. 195.0( 1 Vote )

Prove that: <a na

Answer :

To prove:


We will consider the LHS, so


LHS =


Now let


So we need to need to find first x+y


As per our assumption,



Taking cos on both sides, we get



Taking square on both sides, we get




Now we know sin2x+cos2x=1 cos2x=1-sin2x, so the above equation becomes,






Taking square root on both sides, we get



As per another assumption,



Taking cos on both sides, we get



Taking square on both sides, we get




Now we know sin2x+cos2x=1 cos2x=1-sin2x, so the above equation becomes,






Taking square root on both sides, we get



Now we know,


Cos (x+y)=cos x cos y-sin x sin y


Now substituting values from equation (i), (ii), (iii) and (iv), we get






Now taking cos-1 on both sides, we get



Now substituting the values of x and y, we get



Hence Proved


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