SOLUTION: verify sec(α+β)=secαsecβ/1-tanαtanβ

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Question 807575: verify sec(α+β)=secαsecβ/1-tanαtanβ
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
verify sec(α+β)=secαsecβ/1-tanαtanβ
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start with left side:
sec%28a%2BB%29=%28sec%28a%29sec%28B%29%29%2F%281-tanatanB%29
sec%28a%2BB%29=1%2Fcos%28a%2BB%29
Identity: cos(a+B)=cos(a)cos(B)-sin(a)sin(B)
sec%28a%2BB%29=1%2F%28cos%28a%29cos%28B%29-sin%28a%29sin%28B%29%29
multiply top and bottom by 1/cos(a)cos(B)

sec%28a%2BB%29=sec%28a%29sec%28B%29%2F%281-sin%28a%29sin%28B%29%2Fcos%28a%29cos%28B%29%29%29
sec%28a%2BB%29=sec%28a%29sec%28B%29%2F%281-tan%28a%29tan%28B%29%29%29
verified:
left side=right side