How to prove the following identities cos(30°)-cos(60°)\cos(30°)+sin(60°)=tan(15°)?

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Answer 1 · 2018-08-12T18:29:07

A Proof is given in The Explanation.

$color(red){"The Correct Problem is to prove that,"}$

$color(red)[(cos30^@-cos60^@)/(cos30^@+cos60^@)=tan15^@]$ .

$"The Expression"=(cos30^@-cos60^@)/(cos30^@+cos60^@)$ ,

$={-2sin((30^@+60^@)/2)sin((30^@-60^@)/2)}/{2cos((30^@+60^@)/2)cos((30^@-60^@)/2)}$ ,

$={-2sin45^@sin(-15^@)}/{2cos45^@cos(-15^@)}$ ,

$=(1/sqrt2*sin15^@)/(1/sqrt2*cos15^@)$ ,

$=tan15^@$ , as desired!