Question

log[(sectheta +tan theta) (sectheta -tantheta)]=__
a)1
b)0
c)sec^2theta - tan^2theta
d)not defined
​

Answer 1

Answer:

Answer:

• zero

Formulae used:

• Sec²x-tan²x=1

Solution:

It is given that,

⟹ log[(sectheta+tan theta)(sectheta-tan theta)]

⟹ log[(sec² theta-tan² theta)]

By using the identity,

⟹ log[(1)]

⟹ 0

Answer 2

Answer :-

• Answer is zero.

Step by Step Explanation :-

${log\:(sec\:\theta \: + tan \:\theta)(sec\:\theta \: - tan \:\theta)}$

We know that :-

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

And ,

$⇒{sec}^{2} \theta - {tan}^{2} \theta \: = 1$

So ,

$\sf{⇒log\:\big((sec\:\theta \: + tan \:\theta)(sec\:\theta \: - tan \:\theta)\big)}$

$\sf{⟹ log\:({sec}^{2} \theta - {tan}^{2} \theta \:)}$

$\bullet\sf{log\:(1)}$

And we know that log(1) = 0

So the answer is zero.