If x+y=45°, prove that

Question

{(cotx+1)(coty+1)}/{cotx×coty}=2
Please help me in this TRIGONOMETRY problem.
From the topic - TRIGONOMETRY Ratios of compound angles

Answer 1

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

Answer 2

Good

Answer 3

Well

Answer 4

Q.n : If x+y = 45 Then prove that :(cotx+1)(coty +1)/cotx.coty=2
we have x + y = 45
Now,multiplying by cot on both sides
or,cot(x+y)=cot45
or,cotx.coty -1/cotx + coty =1
or,cotx.coty -1= cotx + coty
or,cotx.coty =cotx + coty + 1
Adding cotx.coty on both sides

or,cotx.coty + cotx.coty =cotx +coty +1+cotx.coty
rearranging on right side,
or,2cotx.coty =cotx.coty + cotx +coty + 1
or,2cotx.coty = cotx (coty + 1) +1(coty + 1)
Or,2 =(cotx +1)(coty +1)/cotx.coty
or,(Cotx+1)(coty+1)/cotx.coty=2
proved

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