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Trigonometric Ratios in terms of the value of one of them
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Trigonometric Ratios in terms of the value of one of them
Here, you will find the trigonometric ratios when one of the trigonometric ratio is given.
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Example: If sec = y + 1/4y, Prove that
      sec + tan = 2y or , 1/2y
Solution: you have sec = y + 1/y
tan2= sec2 - 1
tan2 = (y + 1/y)2 - 1
tan2 = y2 + (1/16y2) +1/2 - 1
tan2 = y2 + (1/16y2)  - 1/2
tan2 = (y - 1/4y)2
tan = (y - 1/4y)
tan = (y - 1/4y), or tan = -(y - 1/4y)
When tan = y - 1/4y, you have
sec + tan = y + 1/4y + y - 1/4y = 2y
when tan = -(y - 1/4y), you have
sec + tan = (y + 1/ 4y) - (y - 1/ 4y)= 2/ 4y = 1/2y
Hence, sec + tan = 2y or 1/2y
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