Question

The value of cos 75° cos 15° is equal to ?​

Answer 1

Answer:

$\huge\bf\underline\green{Solution:}$

$\bf\purple{cos\:75\:cos\:15}$

$\bf\purple{=cos\:75\:cos\:15(90 - 75)}$

$\bf\purple{=cos\:75\:sin\:75}$

$\bf\purple{ = \frac{1}{2} ( 2sin \:75 \: cos \:75)}$

$\bf\purple{ = \frac{1}{2} Sin\:150}$

$\bf\purple{ = \frac{1}{2} Sin(180-30) }$

$\bf\purple{= \frac{1}{2} Sin30}$

$\bf\purple{\implies \frac{1}{2} \times \frac{1}{2} }$

$\bf\purple{\implies \frac{1}{4} }$

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Hope it will be helpful :) ....✍️

Answer 2

Given: cos 75° cos 15°

To find: The value of cos 75° cos 15°

Solution:  

In the question, the term cos 15° can also be written as cos (90-75)° which can further be written as sin 75°. Hence, the given question can be restated as follows.

$cos 75 cos 15 = cos 75 sin 75$

Now, the number 2 is multiplied and divided by the term obtained.

$cos 75 sin 75= \frac{1}{2}(2cos 75 sin 75)$

The following formula is used to evaluate further.

$2 sin A cos A = sin 2A$

$\frac{1}{2}(2cos 75 sin 75) = \frac{1}{2} (sin 150)$

In order to find the value of sine in a simpler manner, the following calculations are done.

$\frac{1}{2} (sin 150) = \frac{1}{2} (sin (180-30))$

                $= \frac{1}{2} sin 30$

                $= \frac{1}{2}* \frac{1}{2}$

                $= \frac{1}{4}$

Therefore, the value of cos 75° cos 15° is 1/4.