# Prove the identity: secx(1+cosx) = 1+secx

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### 2 Answers

The identity sec x*(1 + cos x) = 1 + sec x has to be proved

sec x*(1 + cos x)

=> (1/cos x)*(1 + cos x)

=> 1/cos x + 1

=> sec x + 1

=> 1 + sec x

**This proves that sec x*(1 + cos x) = 1 + sec x**

L.S. = secx(1+cosx)

=secx+secxcosx

=1/cosx+1/cosx cosx

=1/cosx+cosx/cosx

=1/cosx+1

=2/cosx

R.S. = 1+secx

=1+1/cosx

=2/cosx

Therefore, LS = RS