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Range of Trigonometric Ratios from 0 to 90 Degrees

Evaluate tan...

Question

Evaluate
$\frac{t a n 45^{o}}{c o s e c 30^{o}} + \frac{s e c 60^{o}}{c o t 45^{o}} - \frac{5 s i n 90^{o}}{2 c o s 0^{o}}$

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Solution

$\frac{t a n 45^{o}}{c o s e c 30^{o}} + \frac{s e c 60^{o}}{c o t 45^{o}} - \frac{5 s i n 90^{o}}{2 c o s 0^{o}}$
As we know all the values which is
given here.
$= \frac{1}{2} + \frac{2}{1} - \frac{5}{2}$
$= \frac{5}{2} - \frac{5}{2}$
$= 0$

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\frac{s i n 30^{o}}{s i n 45^{o}} + \frac{t a n 45^{o}}{s e c 60^{o}} - \frac{s i n 60^{o}}{c o t 45^{o}} - \frac{c o s 30^{o}}{s i n 90^{o}}

Q. Evaluate the following.

\frac{cos 45^{o}}{sec 30^{o} + cosec 30^{o}}

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\frac{{cot}^{2} 30^{o} + 4 {sin}^{2} 45^{o} + 3 {sec}^{2} 30^{o} + 5 {cos}^{2} 90^{o}}{sec 60^{o} + c o s e c 30^{o} - {tan}^{2} 60^{o}}

\frac{sin 30^{o} + tan 45^{o} - csc 60^{o}}{cot 45^{o} + cos 60^{o} - sec 30^{o}}

\frac{c o s 45^{o}}{s e c 30^{o}} + c o s e c 30^{o}

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