Trigonometry: Finding the values of Trigonometric Ratios

 Finding the values of Trigonometric Ratios Example: If 3 cot = 2, find the value of(5 cos - 2 sin)/(5 cos + 3 sin). Solution: Given, 3 cot = 2 cot = 2/3. Now, (5 cos - 2 sin)/(5 cos + 3 sin). = [(5 cos - 2 sin)/sin]/[(5 cos + 3 sin)/sin] = [(5 cos/sin)-(2 sin/sin)]/[(5 cos/sin)+(3 sin/sin)] = (5 cot- 2)/(5 cot+ 3) = (5 x 2/3 - 2)/(5 x 2/3 + 3) = (10 - 6)/(10 + 9) = 4/19
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Example: If tan= 3/4, find the value of (1 + sin)/(1 - sin).
Solution: Given, tan= 3/4
 sec
= (1 + tan2
= (1 + (3/4)2
= (25/16)
= 5/4
Therefore,
cos = 1/sec = 4/5
and
sin = (1 - cos2) = (1 - (4/5)2) = 3/5

Thus,
 (1 + sin)/(1 - sin) = (1 + 3/5)/(1 - 3/5) = (8/5)/(2/5) = 8/2 = 4.

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