math
posted by sai vishnu on .
If cos25+sin25=k then the value os cos20 is ?

cos20 = cos(7050) = cos70cos50 + sin70sin50
cos25+sin25 = √2 sin70 = k, so
sin70 = k/√2
cos70 = √(2k^2) / √2
cos^2 25 + 2sin25cos25 + sin^2 25 = k^2
1 + sin50 = k^2
sin50 = k^21
cos50 = k√(2k^2)
so, now we have
cos 20 = k√(2k^2)√(2k^2) / √2 + k(k^21)/√2
= (k(2k^2) + k(k^21))/√2
= k/√2