Question

Find the
Prove that sin theta tan theta= (1 + sec theta)(1 - cos theta)
​

Answer 1

Answer:

Step-by-step explanation:

RHS = (1 +Sec Ф)(1 - Cos Ф)

       = 1*1 -  1*Cos Ф + Sec Ф *1 - Sec Ф *Cos Ф

      = 1 - Cos Ф + Sec Ф - 1              {Sec Ф = $\frac{1}{Cos \ theta}$ )

       =Sec Ф - Cos Ф

       = $\frac{1}{Cos \ theta}$ - Cos Ф

       $= \frac{1}{Cos \ theta}-\frac{Cos \ theta*Cos \ theta}{Cos \ theta}\\\\= \frac{1-Cos^{2} \ theta}{Cos \ theta}\\\\= \frac{Sin^{2} \ theta}{Cos \ theta}\\\\=\frac{Sin \ theta*Sin \ theta}{Cos \ theta}\\\\= Sin \ theta*\frac{Sin \ theta}{Cos \ theta}$

        = Sin  Ф* tan  Ф = LHS

Answer 2

Sin tita tan tita = LHS