The value of tan 45 deg plus theta is equal to

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$\cot (45 ° - θ)$

$\cot (45 ° + θ)$

$\frac{1 + \tan θ}{1 - \tan θ}$

answer is A, C.

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Detailed Solution

The problem asks us to find the value of tan(45° + θ). To solve this, we use the tan addition formula from trigonometry:

tan(A + B) = (tan A + tan B) / (1 - tan A · tan B)

Here, A = 45° and B = θ.

Solution

Formula Application:
Substituting A = 45° and B = θ into the formula:
tan(45° + θ) = (tan 45° + tan θ) / (1 - tan 45° · tan θ)
Value of tan 45°:
From trigonometric tables, we know:
tan 45° = 1
Substitute tan 45° = 1:
tan(45° + θ) = (1 + tan θ) / (1 - 1 · tan θ)
Simplify the Expression:
tan(45° + θ) = (1 + tan θ) / (1 - tan θ)

Final Answer

tan(45° + θ) = (1 + tan θ) / (1 - tan θ)

This is the value of tan(45° + θ) expressed in terms of tan θ.

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