Sponsor Area

Principle Of Mathematical Induction

Question

Prove that:

$cos open parentheses straight pi over 2 plus straight x close parentheses space equals space minus sinx$

Solution

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