The cosine of a sum and cosine of difference identities are (8√6-3)/25 and (8√6+3)/25 respectively
Given the trigonometry functions:
cos s = -4/5 and sint = 1/5
To find cos(s - t):
cos (s +t) = cos s cost - sins sint
cos(s - t) = cos s cost + sins sint
Get the value of cost and sins
According to SOH CAH TOA identity;
cos s = -4/5 = adj/hyp
hyp^2 = opp^2 + adj^2
5^2 = 4^2 + opp^2
opp^2 = 25 - 16
opp^2 = 9
opp = 3
sin s = opp/hyp
sin s = 3/5
Similarly for cos t
sin t = 1/5 = opp/hyp
ad^2j = 5^2 - 1^2
adj^2 = 25 - 1
adj^2 = 24
adj = 2√6
Get cost:
cost = adj/hyp = -2√6/5 (quadrant II)
Recall that cos (s +t) = cos s cost - sins sint
cos (s +t) = -4/5(-2√6/5) - (3/5)(1/5)
cos(s+t) = 8√6/25 - 3/25
cos(s+t) = (8√6-3)/25
Similarly, cos(s-t) = (8√6+3)/25
Hence the cosine of a sum and cosine of difference identities are (8√6-3)/25 and (8√6+3)/25 respectively
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