if 7 sinA -24 cosecA= 0 then find the value of secA
Answers
Given : 7 sinA -24 cosecA= 0
To Find : value of secA
Solution:
7 sinA -24 cosecA= 0
=> 7 sinA = 24 cosecA
=> 7 sinA = 24/SinA
=> Sin²A = 24/7
=> Sin²A > 1
Which is not possible
Hence data is incorrect
if
7 CosecA -24 SinA= 0
=> Sin²A = 7/24
Cos²A = 1 - Sin²A
=> Cos²A = 1 - 7/24
=> Cos²A = 17/24
=> Sec²A = 24/17
=> SecA = ±√(24/17)
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Correct Question :- If 7 sin A - 24 cos A = 0 then find the value of sec A ?
Solution :-
→ 7•sinA - 24•cosA = 0
→ 7•sinA = 24•cosA
→ sinA/cosA = 24 / 7
→ tanA = 24 / 7
→ P / B = 24 / 7
so, using pythagoras theorem,
→ H = √(P² + B²)
→ H = √(24² + 7²)
→ H = √(576 + 49)
→ H = √(625)
→ H = 25
then,
→ secA = H / B
→ sec = (25 / 7) (Ans.)
____________
if we try to solve given question :-
→ 7sinA - 24cosecA = 0
→ 7sinA = 24cosecA
→ 7sinA = 24/sinA
→ 7sin²A = 24
→ sin²A = 24/7
→ sinA = √(24/7)
→ sinA = √24 / √7 => P / H
here,
- P > H . which is not Possible.
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