Question

4. If the product of the intercepts made by the straight line x tan a + y sec a = 1
the coordinate axes is equal to sin a , find a
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Answer 1

Answer:

45° or π/4

Step-by-step explanation:

x tanA + y secA = 1 → x/cotA + y/cosA = 1

Compare this with x/a + y/b = 1, where a and b are intercepts by x-axis and y-axis respectively.

So, intersepts are cotA and cosA.

Product of intersepts is sinA:

=> cotA.cosA = sinA

=> cotA = tanA

=> cotA = cot(90° - A)

=> A = 90° - A

=> A = 45° or π/4

One of the satisfying values is π/4 or 45°. Angle can be kπ/2 + π/4 where k is integer.

Answer 2

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