Question

. If √3 tan ● =1 then evaluate (cos^2 ● - sin^2 ●). imagine● as pheta​

Answer 1

Answer:

Correct option is

A

0.5

3

tanθ=1

⇒tanθ=

3

1

⇒θ=60°

∴sin

2

θ−cos

2

θ=sin

2

θ−cos

2

θ

=(

2

3

)

2

−(

2

1

)

2

=

4

3

−

4

1

=

2

1

Hence, the answer is 0.5.

Answer 2

Answer:

$\red {Value \: of \: sin^{2}\theta - cos^{2}\theta }\green {= \frac{ \sqrt{3}-1}{2}}$

Step-by-step explanation:

$Given \: \sqrt{3} \: tan\theta = 1$

$\implies tan \theta = \frac{1}{\sqrt{3}}\:$

$\implies tan\ \: theta = tan \: 30$

$\implies \theta = 30\degree$

$</p><p>\red {Value \: of \: sin2\theta - cos2\theta }$

$\begin{gathered} = sin 2\times 30 - cos 2\times 30 \\= sin 60 - cos 60\\= \frac{\sqrt{3}}{2} - \frac{1}{2}\\= \frac{ \sqrt{3}-1}{2}\end{gathered}$

$Therefore,</p><p></p><p>\red {Value \: of \: sin2\theta - cos2\theta } \\ Valueofsin2θ−cos2θ</p><p></p><p>\green {= \frac{ \sqrt{3}-1}{2}}$