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vaieri [72.5K]
3 years ago
6

Sec squared 55 - tan squared 55

Mathematics
1 answer:
sergejj [24]3 years ago
6 0

<u>Answer: </u>

sec squared 55 – tan squared 55  = 1

<u>Explanation:</u>

Given, sec square 55 – tan squared 55

We know that,

\sec \Theta=\frac{\text {hypotenuse}}{\text {base}}

And,

\tan \theta=\frac{\text { perpendicular }}{\text { base }}

where Ө is the angle

Substituting the values

\left(\frac{\text {hypotenuse}}{\text {base}}\right)^{2}-\left(\frac{\text { perpendicular }}{\text {base}}\right)^{2}

Solving,

\frac{(\text {hypotenuse})^{2}-(\text {perpendicular})^{2}}{(\text {base}) *(\text {base})}

According to Pythagoras theorem,

\text { (hypotenuse) }^{2}-\text { (perpendicular) }^{2}=(\text { base })^{2}

Putting this in the equation;

squared 55 - tan squared 55 =

\frac{(\text {hypotenuse})^{2}-(\text {perpendicular})^{2}}{(\text {base}) *(\text {base})}=\frac{(\text {base})^{2}}{(\text {base}) *(\text {base})}=1

Therefore, sec squared 55 – tan squared 55 = 1

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