Question

if a trigonometric ratio of an angle is known we can find all remaining ratios ' explain whether this statement is ture or false.

Answer 1

Yeah its true. Such as let us take cot A . Tan A can be expressed as the reciprocal of cot A . Tan A =1\cot A Also 1+ cot2 A = cosecA2 . And also cosecA = Square root of cot2 A - 1 .
Again sin is expressed as the opposite of cosecA. So SinA = 1/ CosecA = 1\Square root of cot2 A -1 . Cos2A + Sin2A = 1 . So cosa = Square root of Sin2A -1. Lastly SecA is the opposite of CosA . So Sec A = 1\cosA .

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Answer 2

Answer:

Yes it is true because if you know one trigonometric ratio than you know two sides of a right angled triangle. Thus you can find the third side and subsequently the other trigonometric ratios.