☆☆☆☆Need help☆☆☆☆
If A+B = 45°, then (1+tan A)(1+tanB) should be equal to ___________.
Explain your answer.
Answers
Answered by
4
Hey !!!
A + B = 45° (given )
➡ As, (1 + tanA ) ( 1 + tanB)
= (1 + 1/cotA ) (1 + 1 /cotB )
= (cotA + 1 /cotA ) ( 1 +1 /cotB)
= (cotA + 1 /cotA ) ( 1+1/cot ( 45° - A)
(•°• A + B = 45°)
= (cotA + 1 /cotA ){ 1 +( cotA - cot45° /cot45° ×cotA + 1 )}
=•°•cot(A+ B) = cotA ×cotB + 1 /cotB - cotA
using this identity
= cotA + 1 /cotA{ ( 1 + (cotA -1 /cotA +1}
= cotA + 1 /cotA {( cotA +1 + cotA -1 )} /cotA +1
= (cotA + 1 /cotA )(cotA+ 1 + cotA -1 )/cotA + 1
= ( cotA + 1 /cotA) ( 2cotA/cotA +1 )
= then( cotA+ 1 ) cancelled . and cotA is also cancelled from numerator to denominator
remaining 2
so, the answer is 2
*******************************
Hope it helps you !!!
@Rajukumar111
A + B = 45° (given )
➡ As, (1 + tanA ) ( 1 + tanB)
= (1 + 1/cotA ) (1 + 1 /cotB )
= (cotA + 1 /cotA ) ( 1 +1 /cotB)
= (cotA + 1 /cotA ) ( 1+1/cot ( 45° - A)
(•°• A + B = 45°)
= (cotA + 1 /cotA ){ 1 +( cotA - cot45° /cot45° ×cotA + 1 )}
=•°•cot(A+ B) = cotA ×cotB + 1 /cotB - cotA
using this identity
= cotA + 1 /cotA{ ( 1 + (cotA -1 /cotA +1}
= cotA + 1 /cotA {( cotA +1 + cotA -1 )} /cotA +1
= (cotA + 1 /cotA )(cotA+ 1 + cotA -1 )/cotA + 1
= ( cotA + 1 /cotA) ( 2cotA/cotA +1 )
= then( cotA+ 1 ) cancelled . and cotA is also cancelled from numerator to denominator
remaining 2
so, the answer is 2
*******************************
Hope it helps you !!!
@Rajukumar111
Attachments:
allysia:
nope
Answered by
7
HELLO DEAR,
we know that:-
(A + B) = 45°
=> tan(A + B) = tan45°
I HOPE ITS HELP YOU DEAR,
THANKS
we know that:-
(A + B) = 45°
=> tan(A + B) = tan45°
I HOPE ITS HELP YOU DEAR,
THANKS
Similar questions