Question

If sec theta +tan theta +1 =0, then sec theta minus tan theta is

Answer 1

Answer:

Please see the attachment

Answer 2

Concept: A branch of mathematics called trigonometry looks at how triangle side lengths and angles relate to one another. A common angle in trigonometry has six different functions. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec) are their names.

Given: sec θ + tan θ + 1 = 0

To find: sec θ - tan θ

Solution: As we know that

$sec^{2}$ θ - $tan^{2}$ θ = 1

(sec θ + tan θ) (sec θ - tan θ) = 1                    [since $a^{2} - b^{2} = (a+b) (a-b)$]

It is given that sec θ + tan θ + 1 = 0

sec θ + tan θ = -1

Putting the value of sec θ + tan θ = -1 in (sec θ + tan θ) (sec θ - tan θ) = 1, we get

-1 (sec θ - tan θ) = 1

(sec θ - tan θ) = -1

Hence, (sec θ - tan θ) = -1

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