Question

13. If sec + tan 0+1=0 then (sec 0 -tan 0) = ?
(a) 1
(b)-1
(c) 0
​

Answer 1

$\large {\underline{\bf{ question}}}$

$\tt{if \: sec \theta + tan \theta + 1 = 0 }$

$\tt{then \: (sec \theta - tan \theta = \: \: )}$

a) 1

b) -1

c) 0

$\large{ \underline{ \bf{solution}}}$

We have

$\tt{sec \theta + tan \theta + 1 = 0 }\\ \\ \tt{sec \theta \: + tan \theta = - 1}$

$multiplying \: by \: sec \theta - tan \theta \: both \: sides$

$\tt{(sec \theta +tan \theta)(sec \theta - tan \theta) = - 1(sec \theta - tan \theta) } \\ \\ \tt{ {sec}^{2} \theta - {tan}^{2} \theta = - 1(sec \theta - tan \theta) }$

using identity

${sec}^{2} \alpha - {tan}^{2} \alpha = 1$

$\tt {1 = - 1(sec \theta - tan \theta)}$

$\boxed{\bf{sec \theta - tan \theta = - 1}}$

Hence,

the correct option is (b) -1.

Answer 2

Answer:

I hope this solution from Educart helps.