Question

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

Answer 1

Answer:

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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