Question

find an acute angle theta when cos theta -sin theta/cos theta+sin theta=1-√3/1+√3

Answer 1

#chinimalik30 I am sorry for delay
Here is the solution
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Answer 2

An acute angle of theta is 60 degree.

To find:

Acute angle theta = ?

Solution:

Given: $\frac{\cos \theta-\sin \theta}{\cos \theta+\sin \theta}=\frac{1-\sqrt{3}}{1+\sqrt{3}}$  

Applying componendo dividendo, we get

$\frac{\cos \theta-\sin \theta+\cos \theta+\sin \theta}{\cos \theta-\sin \theta-\cos \theta \mp \sin \theta}=\frac{1-\sqrt{3}+1+\sqrt{3}}{1-\sqrt{3}-1 \mp \sqrt{3}}$

$\frac{-2 \cos \theta}{2 \cos \theta}=\frac{2}{-2 \sqrt{3}}$

$\cos \theta=\frac{2}{\sqrt{3}}$

$\theta=60\ degree$

An acute angle is an angle smaller than a right angle. The range of acute angle is one that is less than “90 degrees”. Trigonometric functions of an acute angle are “ratios of the different pairs of sides” of a “right-angled triangle”.