Question

If_/3tan theta = 1 then find the value of sin 2 theta - cos 2theta.

Answer 1

root3 tan theta=1
tan theta=1/root3
theta=30degree
now
sin2theta -cos2theta
=sin (2x30)-cos (2x30)
=sin60-cos60=root3/2-1/2=(root3-1)/2

Answer 2

Answer:

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

Step-by-step explanation:

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

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

$\implies tan\theta = tan 30\degee$

$\implies \theta = 30\degree$

$\red {Value \: of \: sin2\theta - cos2\theta }$

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

Therefore.,

$\red {Value \: of \: sin2\theta - cos2\theta }$

$\green {= \frac{ \sqrt{3}-1}{2}}$

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