Question 605241
1.Derive a formula for cos 2A with aid of
 cos (A + B).
<pre>
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

Substitute A for B

cos(A + A) = cos(A)cos(A) - sin(A)sin(A)

Simplifying,

cos(2A) = cosē(A) - sinē(A)

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</pre>
2.Prove that 

2·tan(x) + 2·cot(x) = {{{4/sin(2x)}}}
<pre>
2·{{{sin(x)/cos(x)}}} + 2·{{{cos(x)/sin(x)}}}

{{{2sin(x)/cos(x)}}} + {{{2cos(x)/sin(x)}}}

Get LCD of sin(x)cos(x)

{{{(2sin^2(x) + 2cos^2(x))/(sin(x)cos(x))}}}

{{{(2(sin^2(x) + cos^2(x)))/(sin(x)cos(x))}}}

{{{(2(1))/(sin(x)cos(x))}}}

{{{ 2/( sin(x)cos(x) ) }}}

Multiply by {{{2/2}}}

{{{4/(2sin(x)cos(x))}}}

{{{4/sin(2x)}}}

Edwin</pre>