Question

$if \: \sin(theta) + \cos(theta) = \sqrt{2} then \: find \: the \: value \: of \: \tan(theta) .$
pls solve the question in the attachment ​

Answer 1

I am taking theta to beO

sinO + cosO = √2

divide everything by cosO

sinO/cosO + cosO/cosO = √2/cosO

tanO + 1 = √2secO

square both of the side

tan²O + 1 + 2tanO = 2sec²O

tan²O + 1+2tan O = 2(1+tan²O)

2tanO = tan²O + 1

tan²O - tanO - tanO + 1

tanO( tanO -1) -1 (tanO -1)

tanO = 1