Пусть ctg x =-7/24 найдите cos x/2

Question

Пусть ctg x =-7/24 найдите cos x/2

Answer 1

Sin²x=1:(1+ctg²x)=1:(1+49/576)=1:625/576=576/625
cos²x=1-sin²x=1-576/625=49/625
cosx=+-7/25
1)cosx=-7/25
cosx/2=√[(1+cosx)/2]
cosx/2=√[(1-7/25)/2]=√(9/25)=3/5
2)cosx=7/25=√[(1+7/25)/2]=√(16/25)=4/5