Question

tan(45+a)-tan(45-a)=2tan2a

Answer 1

hello users ....
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we know that:
tan (45° + x ) = (1 + tan x ) / (1 - tan x )
and
tan ( 45° - x ) = (1 - tan x ) / ( 1 + tan x )
and
tan (x + y) = (tan x + tan y) / (1 - tan x .tan y )

solution :-
taking LHS,
tan ( 45° + a) - tan (45° - a)
= (1 + tan a ) / (1 - tan a ) - (1 - tan a ) / ( 1 + tan a )

now,taking LCM
= [ (1 + tan a ) ( 1 + tan a ) - (1 - tan a ) ( 1 - tan a ) ] / (1 - tan a ) ( 1 + tan a )

= [ (1 + tan a )² - ( 1 - tan a )²] / (1 - tan²a)

= [ (1 + tan²a + 2tan a ) - ( 1 + tan²a - 2tan a) ] / ( 1 - tan²a )

= [ (1 + tan²a + 2tan a - 1 - tan²a + 2tan a ) ] / ( 1 - tan²a )

= ( 4tan a ) / ( 1 - tan²a)

= 2 × 2tan a / ( 1 - tan²a)

now,
taking RHS,
2 tan 2a = 2 tan ( a + a )

= 2 × ( tan a + tan a ) / ( 1 - tan a .tan a)

= 2 × 2tan a / ( 1 - tan²a )

Hence,
LHS = RHS
Proved....


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✡✡ hope it helps ✡✡

Answer 2

Answer:

which rank is math aryabhatta

Step-by-step explanation:

in brainly ??