What is the value of (1-tan^2(15))/(1+tan^2(15)) ?

The value of (1-tan^2(15))/(1+tan^2(15)) is (sqrt(3))/2

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(1-tan^2(15))/(1+tan^2(15))

\frac{1 - tan ^{2} ( 1 5 ^{\circ} )}{1 + tan ^{2} ( 1 5 ^{\circ} )}

\frac{3}{2}

Solution steps

\frac{1 - tan ^{2} ( 1 5 ^{\circ} )}{1 + tan ^{2} ( 1 5 ^{\circ} )}

Rewrite using trig identities:

tan^{2} (1 5^{\circ}) = \frac{1 - cos ( 3 0 ^{\circ} )}{1 + cos ( 3 0 ^{\circ} )}

= \frac{1 - \frac{1 - c o s ( 3 0 ^{\circ} )}{1 + c o s ( 3 0 ^{\circ} )}}{1 + \frac{1 - c o s ( 3 0 ^{\circ} )}{1 + c o s ( 3 0 ^{\circ} )}}

Simplify

= cos (3 0^{\circ})

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

= \frac{3}{2}

π (0.04)^{2} cos (3 0^{\circ}) (- 0.2)

- csc (3 0^{\circ})

6 sin (3)

5 cos (18 0^{\circ})

cos (17 5^{\circ})

What is the value of (1-tan^2(15))/(1+tan^2(15)) ?
The value of (1-tan^2(15))/(1+tan^2(15)) is (sqrt(3))/2