13sin theta=12find sectheta - tantheta
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Answer :
sec∅ - tan∅ = 1/5
Note :
★ sin∅ = p/h
★ cos∅ = b/h
★ tan∅ = p/b
★ cosec∅ = 1/sin∅ = h/p
★ sec∅ = 1/cos∅ = h/b
★ cot∅ = 1/tan∅ = b/p
★ Pythagoras theorem : In a right angled triangle , h² = p² + b²
Where p = perpendicular
b = base
h = hypotenuse
Solution :
- Given : 13sin∅ = 12
- To find : sec∅ - tan∅ = ?
We have ;
=> 13sin∅ = 12
=> sin∅ = 12/13
Here ,
Perpendicular , p = 12
Hypotenuse , h = 13
Now ,
Applying Pythagoras theorem , we have ;
=> h² = p² + b²
=> b² = h² - p²
=> b² = 13² - 12²
=> b² = (13 + 12)•(13 - 12)
=> b² = 25•1
=> b² = 25
=> b = √25
=> b = 5
Now ,
• sec∅ = h/b = 13/5
• tan∅ = p/b = 12/5
Thus ,
=> sec∅ - tan∅ = 13/5 - 12/5
=> sec∅ - tan∅ = (13 - 12)/5
=> sec∅ - tan∅ = 1/5
Hence ,
sec∅ - tan∅ = 1/5
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