Sponsor Area

Principle Of Mathematical Induction

Question

Prove that:

$sin open parentheses straight pi over 2 plus straight x close parentheses space equals space cosx$

Solution

sin (x+y) = sinx cosy + cosx siny
Replacing x by $WiredFaculty$ and y by x, we get
$sin open parentheses straight pi over 2 plus straight x close parentheses space equals space sin open parentheses straight pi over 2 close parentheses cosx space plus space cos open parentheses straight pi over 2 close parentheses sinx space equals space left parenthesis 1 right parenthesis space left parenthesis cosx right parenthesis space plus space 0 space left parenthesis sinx right parenthesis space equals space cosx$
Hence, $WiredFaculty$