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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