Question

1-tan^2 a = 2 - sec^2a​

Answer 1

Step-by-step explanation:

...... Answer is in attachment.......

Answer 2

Given:-

1-tan^2 a = 2 - sec^2a

Find:-

2 - sec^2a

Answer:-

Take left hand side of the equation

$\sf \: (1 + tan \:A)^2 + (1 - tan \:A)^2 = { \underline{ \boxed{ \red { \sf{2sec^2 \: A.}}}}}$

$\sf \: LHS = (1 + tan \: A)^2 + (1 - tan \: A)^2 = 1 +$

$\sf \: tan^2A + 2 \: tan \: A + 1 + tan^2 \: A -{ \underline{ \boxed{ \blue{ \sf {2 \: tan \: A}}}}}$

$\sf \: = 2 + 2 \: tan ^{2} A$

$\sf= 2(1 + tan ^{2} A)$

$\sf = 2 \: sec {}^{2} A$

=RHS