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यदि `x+y+z=(pi)/(2)` तो सिद्ध कीजिए कि `cos(x-y-z)+cos(y-x-z)+cos(z-x-y)=4cos x cos y cos z` |
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Answer» बायाँ पक्ष `=2cos((x-y-z+y-x-z)/(2))cos((x-y-z-y+x+z)/(2))+cos(z-x-y)` `=2cos(-z)cos(x-y)+cos(z-x-y)` `=2cos z cos (x-y)+cos[z-((pi)/(2)-z)]` `=2cos z cos (x-y)+cos[-((pi)/(2)-2z)]` `=2cos z cos (x-y)+sin 2z` `=2cos z cos (x-y)+2sin z cosz` `=2cos z[cos (x-y)+sinz]` `=2cos z[cos(x-y)+sin((pi)/(2)-bar(x+y))]` `=2cos z [cos(x-y)+cos (x+y)]` `=2cos z.2 cos x cosy` `=4 cos x cos y cosz= `दायाँ पक्ष |
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