Posted by **sai vishnu** on Thursday, May 2, 2013 at 1:03am.

If cos25+sin25=k then the value os cos20 is ?

- math -
**Steve**, Thursday, May 2, 2013 at 3:08pm
cos20 = cos(70-50) = cos70cos50 + sin70sin50

cos25+sin25 = √2 sin70 = k, so

sin70 = k/√2

cos70 = √(2-k^2) / √2

cos^2 25 + 2sin25cos25 + sin^2 25 = k^2

1 + sin50 = k^2

sin50 = k^2-1

cos50 = k√(2-k^2)

so, now we have

cos 20 = k√(2-k^2)√(2-k^2) / √2 + k(k^2-1)/√2

= (k(2-k^2) + k(k^2-1))/√2

= k/√2

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