Which of the following is true: * 1 point sin A + cosec A = 1 sin A + cos A = 1 sin A cot A = 1 cos A sec A = 1
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Answer:
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cos A sec A = 1 is the true statement.
As we are given,
1.) Sin A + Cosec A = 1
Taking the Left-Hand Side of the statement given,
SinA + CosecA
= SinA + 1/SinA
= Sin²A + 1
SinA
≠ Right Hand Side
Therefore, This statement is false.
2.) Sin A + Cos A = 1
Taking the Left-Hand Side of the statement given,
SinA + CosA
Taking the square of complete expression
= ( SinA + CosA )²
= Sin²A + Cos²A + 2SinACosA
= 1 + 2SinACosA [Sin²A + Cos²A = 1]
≠ Right Hand Side
Therefore, This statement is false.
3.) Sin A + Cot A = 1
Taking the Left-Hand Side of the statement given,
SinA + CotA
= SinA + 1/TanA
= SinA + CosA/SinA
= Sin²A + CosA
SinA
≠ Right Hand Side
Therefore, This statement is false.
4.) Cos A . Sec A = 1
Taking the Left-Hand Side of the statement given,
CosA . SecA
= CosA * 1/CosA
= 1
= Right Hand Side
Therefore, This statement is True.
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