Question

1) $cos2x=co{s}^{2}x-si{n}^{2}x$

2) $1+sin2x=(cosx+sinx{)}^2$

3) $1-sin2x=(cosx-sinx{)}^2$

How many of the above statements are correct?

Answer 1

These are the relation we learned in trigonometry. We show the derivations

1) $cos2x=cos(x+x)$

$=cosxcosx-sinxsinx$

$=co{s}^{2}x-si{n}^{2}x$

2) $(cosx+sinx{)}^2=co{s}^{2}x+si{n}^{2}x+2sinxcosx$

$=1+sin2x$

3) $(cosx-sinx{)}^2=co{s}^{2}x+si{n}^{2}x-2sinxcosx$

$=1-sin2x$

$\Rightarrow$ All the three statements are correct