Question

Prove that :1-sinx/cosx=cosx/1+sinx

Answer 1

Acc. To Me,

See Below

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Start from LHS

=(1-sinx)/cosx

Rationalise by 1+sinx then

=(1-sinx)(1+sinx)/cosx(1+sinx)

by (a+b)(a-b)=a²-b²

=(1²-sin²x)/cosx(1+sinx)

by 1-sin²x=cos²x  So

=cos²x/cosx(1+sinx)

=cosx/(1+sinx)

LHS=RHS

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I hope you understand my answer