what is the value of
sec(75°)
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sec 75
sec 75 = cosec 90 - 75
cosec 15
sec 75 = cosec 90 - 75
cosec 15
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It's true that this is sec(30+45). This is also 1 / cos(30+45). Now use the addition formula for cosine:
cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
This gives you
1 / [ cos(30)cos(45) - sin(30)sin(45) ] =
1 / [ (√3 / 2)(√2 /2) - (1/2)(√2 / 2) ]
You can simplify this from here
cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
This gives you
1 / [ cos(30)cos(45) - sin(30)sin(45) ] =
1 / [ (√3 / 2)(√2 /2) - (1/2)(√2 / 2) ]
You can simplify this from here
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