Question

If x + y = 45°, prove that:
(cot x + 1)(cot y +1) / (cot x.cot y) = 2

Answer 1

Answer:

Step-by-step explanation:

On the left side:

cot(x+y) = (cotx*coty - 1)/(cotx + coty) = 1

cotx * coty - 1 = cotx + coty

cotx * coty = 1 + cotx + coty

1 = (1 + cotx + coty)/(cotx * coty)

On the right side:

(cotx+1)(coty+1)/(cotx * coty)

= (cotx * coty + cotx + coty + 1)/(cotx * coty)

= 1 + (1 + cotx + coty)/(cotx * coty)

Look back at the left side. What we now have is just

= 1+1

= 2

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