Question

if 3 root tan -1 -0 find the value of sin ² 0 -cos²0
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Answer 1

Given:

√3tan∅-1=0.......................[1]

To find the value of sin²∅ - cos²∅

Consider [1],

√3tan∅-1=0

→√3tan∅=1

→tan∅=1/√3

From the trigonometric table,

tan60=1/√3

Implies,

→tan∅=tan30

Thus,

∅=30°

Now,

sin²∅ - cos²∅

=sin²30 - cos²30

=(1/2)² - (√3/2)²

=1/4 - 3/4

= -2/4

= -1/2

Hence,sin²∅ - cos²∅ = -1/2

Answer 2

SOLUTION

We have,

$\sqrt{3} \: tan \theta = 1 \\ \\ = > tan \theta = \frac{1}{ \sqrt{3} } \\ \\ = > tan \theta = tan \: 30 \\ = > \theta = 30 \degree$

Now,

$= > {sin}^{2} - {cos}^{2} = {sin}^{2} \: 30 - {cos}^{2} \: 30 \\ = >( \frac{1}{2} ) {}^{2} - ( \frac{ \sqrt{3} }{2} ) {}^{2} \\ \\ = > \frac{1}{4} - \frac{3}{4} = \frac{ - 2}{4} \\ \\ = > - \frac{1}{2}$

hope it helps ☺️