Question

The value of cot[π/4 - cot⁻¹3] is......,Select Proper option from the given options.
(a) 3
(b) 7
(c) 9
(d) 3/4

Answer 1

we have to find the value of cot[π/4 - cot^-1(3)]

Let cot^-1(3) = A

then, cotA = 3 .........(1)

now , cot[π/4 - cot^-1(3)] = cot(π/4 - A)

we know, formula , cot(A - B) = (cotA.cotB + 1)/(cotB - cotA)

so, cot(π/4 - A) = (cotπ/4.cotA + 1)/(cotA- cotπ/4)

= (cotA + 1)/(cotA - 1)

now put equation (1),

= (3 + 1)/(3 - 1) = 2

hence, option is incorrect.

answer should be 2

Answer 2

HELLO DEAR,



GIVEN:-
cot[π/4 - cot-¹(3)]

Let cot-¹(3) = A SO, cotA = 3

now , cot[π/4 - cot-¹(3)] = cot(π/4 - A)

WE KNOW, cot(A - B) = (cotA.cotB + 1)/(cotB - cotA)

so, cot(π/4 - A) = (cotπ/4.cotA + 1)/(cotA- cotπ/4)

[as , cotπ/4 = 1]

= (cotA + 1)/(cotA - 1)

AND [cotA = 3]

=> (3 + 1)/(3 - 1) = 2

hence, answer is 2


I HOPE ITS HELP YOU DEAR,
THANKS