Question

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

Answer 1

Sin tita tan tita = LHS

Answer 2

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 =
`(1)/(Cos \ theta)` )

=Sec Ф - Cos Ф

=
`(1)/(Cos \ theta)` - Cos Ф

`= (1)/(Cos \ theta)-(Cos \ theta*Cos \ theta)/(Cos \ theta)\\\\= (1-Cos^(2) \ theta)/(Cos \ theta)\\\\= (Sin^(2) \ theta)/(Cos \ theta)\\\\=(Sin \ theta*Sin \ theta)/(Cos \ theta)\\\\= Sin \ theta*(Sin \ theta)/(Cos \ theta)`

= Sin Ф* tan Ф = LHS