# Prove this using trigonometric identities

### Prove this using trigonometric identities

$$\frac{1}{1+sinx}$$ = $$\frac{secx-sinxsecx}{cosx}$$
Prove this using identities.
nazz

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### Re: Prove this using trigonometric identities

$$secx=\frac{1}{cosx}\Rightarrow \frac{1}{cosx}.\frac{1-sinx}{cosx}=\frac{1-sinx}{cos^{2}x}=\frac{1-sinx}{1-sin^{2}x}=\frac{1}{1+sinx}$$

nathi123

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### Re: Prove this using trigonometric identities

A=$$\frac{secx-sinxsecx}{cosx}=\frac{secx(1-sinx)}{cosx}=\frac{1-sinx}{cos^{2}x}=\frac{1-sinx}{(1-sinx)(1+sinx)}=\frac{1}{1+sinx}$$
$$secx=\frac{1}{cosx}$$.

nathi123

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### Re: Prove this using trigonometric identities

RHS
secx-sinxsecx= secx(1-sinx)=(1-sinx)/cosx
secx-sinxsecx/cosx= (1-sinx)/(cosx)^2
= (1-sinx)/(1- (sinx)^2)
=(1-sinx)/(1+sinx)(1-sinx)

=1/(1+sinx)=LHS
Proved.

Venkatesans

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