Question

if A+B=90° then solve it please ​

Answer 1

Given; A + B = 90 then B = 90 - A and 2B = 180 - 2A

Now, 1+(tanA/tanB) = 1+(tanA * cotB) => 1+(tanA * cot( 90 - A)

==> 1 + tan^2A = sec^2 A [as cot( 90 - A) = tan A]

so, L.H.S. = sec^2 A

R.H.S. = tan^2 A sec^2 B

=> tan^2 A sec^2 (90 - A)

=> tan^2 A cosec^2 A

=> (sin^2 A / cos^2 A) * cosec^2 A

=> (sin^2 A * cosec^2 A) / cos^2 A

=> 1 / cos^2 A ==> sec^2 A

so L.H.S. = R.H.S.

Answer 2

${\huge {\mathfrak {Answer :-}}}$

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Hey mate, Please refer to the attachment above ⬆️ ⬆️

Identities used :

1. sec^2 X - tan^2 X = 1
2. tan X = cot (90° - X)
3. tan X = 1/cot X

Note :- There can be a various number of ways in which the problem can be solved .

Thank you !

Have a nice day..

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