1.

Tan0/(sec0+1)= (sec0-1)/tan0​

Answer»

LHS = \frac{ tan0}{(sec 0 + 1 )} \\=\frac{ tan0(sec 0 - 1)}{(sec 0 + 1 )(sec 0 - 1 )} \\=\frac{ tan0(sec 0 - 1)}{sec^{2} 0 - 1^{2} } \\= \frac{ tan0(sec 0 - 1)}{tan^{2} 0 }

\boxed { \pink { Since, sec^{2} 0 - 1 = tan^{2} 0 }}

= \frac{ (sec 0 - 1)}{tan 0 } \\=RHS

Hence\: proved


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