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Complementary Trigonometric Ratios

Evaluate each...

Question

Evaluate each of the following

sin² 30° cos² 45° + 4 tan² 30° + $\frac{1}{2} \sin^{2} 90 ° - 2 \cos^{2} 90 ° + \frac{1}{24} \cos^{2} 0 °$

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Solution

We have,

…… (1)

Now,

,, ,,

So by substituting above values in equation (1)

We get,

LCM of 8, 3, 2 and 24 is 48

Therefore by taking LCM

We get,

In the above equation the first term gets reduced to

Therefore,

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Similar questions

{sin}^{2} 90. {cos}^{2} 45 + 4 {tan}^{2} 30 + \frac{1}{2} {sin}^{2} a - 2 {cos}^{2} 90 + \frac{1}{24}

Q. Evaluate the following :

s i n^{2} 30^{\circ} c o s^{2} 45^{\circ} + 4 t a n^{2} 30^{\circ} + \frac{1}{2} s i n^{2} 90^{\circ} - 2 c o s^{2} 90^{\circ} + \frac{1}{24} c o s^{2} 0^{\circ}

(\sin^{2} 30 ° \cos^{2} 45 ° + 4 \tan^{2} 30 ° + \frac{1}{2} \sin^{2} 90 ° + \frac{1}{8} \cot^{2} 60 °) = ?

(a) 2
(b) 3
(c) 4
(d)

\frac{5}{2}

Q. The value of

(\sin^{2} 30 ° \cos^{2} 45 ° + 4 \tan^{2} 30 ° + \frac{1}{2} \sin^{2} 90 ° + \frac{1}{8} \cot^{2} 60 °) = ?

\frac{3}{8}

\frac{5}{8}

Evaluate each of the following

$s i n^{2} 30^{o} + s i n^{2} 45^{o} + 4 t a n^{2} 30^{o} + \frac{1}{2} s i n^{2} 90^{o} - 2 c o s^{2} 90^{o} + \frac{1}{24} c o s^{2} 0^{o}$

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