Question

find the value of cos48cos12​

Answer 1

It's value is 1/2

Hope it helps

Answer 2

Concept:

Trigonometry is a discipline of mathematics that investigates the relationship between triangle side lengths and angles.

Given:

cos48°-cos12°

To find:

The value of cos48°-cos12°​

Solution:

An equation is given to us, that is, cos48°-cos12°

We can solve it using the formula $cosA-cosB=-2sin\frac{A+B}{2}) sin(\frac{A-B}{2})$

So, if we would put the values of A and B in the formula we get,

$cos48-cos12=-2sin(\frac{48+12}{2}) sin(\frac{48-12}{2})\\ -2sn30*sin18\\-2*\frac{1}{2}*sin18\\ -sin18$

Now, let's assume the angle is x

$x=18\\2x=36\\sin2x=sin36\\sin2x=sin(90-54)\\sin2x=cos54$

Also, we know another formula

$sin2x=cos3x\\2sinxcosx=cos(4cos^{2}x-3cosx)$

So, if we put the values in this formula then we get

$2sinx=4(1-sin^{2} x-3\\4-4sin^{2}x-3-2sinx=0\\ -4sin^{2} x-2sinx+1=0\\4sin^{2}x+2sinx-1=0$

Now, we get

$sinx=\frac{-2+\sqrt{4+16} }{2*4} \\sinx=\frac{-2-\sqrt{4+16} }{2*4} \\sinx=\frac{-2+\sqrt{5} }{8} \\sinx=\frac{-1+\sqrt{5} }{4}$

Now, cos48°-cos12°= -sin18°

∴sinx= $\frac{1-\sqrt{5} }{4}$

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