Question

9. If A + B = 225º and none of A and B is an
integral multiple of π, prove that
(1 + cot A) (1 + cot B) = 2 cot A cot B (or)
[cot A_1+cot A]
[cot B_
1+cot B]=1/2
​

Answer 1

$\sf{Solution:-}$

Correct Question:-

If A + B = 225 then prove that ( 1 -cotA )( 1 - cotB ) = 2

Formulae to know:-

• cot(A + B ) = cotBcotA - 1 / cotB + cotA

cot 225 ° = cot (180+ 45)

cot225° = cot45°

• cot225° = 1

Solution:-

A + B = 225

Taking "cot" on both sides

cot ( A + B ) = cot225

cotB cotA - 1 / cotB + cotA = 1

cotBcotA -1 = cotB + cotA

cotB cotA - cotB - cotA = 1

- cotA - cotB + cotA cotB = 1

Adding "1" on both sides

1 - cotA - cotB + cotA cotB = 1 + 1

(1 - cotA ) -cotB ( 1 - cotA ) = 2

(1 - cotA) ( 1 - cotB ) = 2

Hence proved

Know more :-

Trigon metric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

csc²θ - cot²θ = 1

Trigometric relations

sinθ = 1/cscθ

cosθ = 1 /secθ

tanθ = 1/cotθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

Trigonmetric ratios

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

cotθ = adj/opp

cscθ = hyp/opp

secθ = hyp/adj