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Relation between Trigonometric Ratios

Evaluate each...

Question

Evaluate each of the following

$\frac{\sin 30 °}{\sin 45 °} + \frac{\tan 45 °}{\sec 60 °} - \frac{\sin 60 °}{\cot 45 °} - \frac{\cos 30 °}{\sin 90 °}$

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Solution

We have,

…… (1)

Now,

,, ,, ,

So by substituting above values in equation (1)

We get,

Now by further simplifying

We get,

Since,

Therefore,

Now, one gets cancelled and

We get,

Now, by taking LCM

We get,

Therefore,

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\frac{sin 30^{\circ}}{sin 45^{\circ}} + \frac{tan 45^{\circ}}{sec 60^{\circ}} - \frac{sin 60^{\circ}}{cot 45^{\circ}} - \frac{cos 30^{\circ}}{sin 90^{\circ}}

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

\frac{sin 30 °}{cos 45 °} + \frac{cot 45 °}{sec 60 °} - \frac{sin 60 °}{tan 45 °} + \frac{cos 30 °}{sin 90 °}

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\frac{\sin 30 °}{\cos 45 °} + \frac{\cot 45 °}{\sec 60 °} - \frac{\sin 60 °}{\tan 45 °} - \frac{\cos 30 °}{\sin 90 °}

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