Question

Sec theta(1 - sin theta) (sec theta+tan theta)=1

Proove

Answer 1

TO PROVE

$\sec( \theta) (1 - \sin( \theta) )( \sec( \theta) + \tan( \theta) ) = 1$

PROOF

LHS =

$\sec( \theta) (1 - \sin( \theta) )( \sec( \theta) + \tan( \theta) ) \\ \\ \\ = \frac{1}{ \cos( \theta) } (1 - \sin( \theta) )( \frac{1}{ \cos( \theta)} + \frac{ \sin( \theta) }{ \cos( \theta) } ) \\ \\ \\ \\ = (\frac{1 - \sin( \theta) }{ \cos( \theta) } )( \frac{1 + \sin( \theta) }{ \cos( \theta) } ) \\ \\ \\ = \frac{ {1}^{2} - { \sin( \theta) }^{2} }{ { \cos( \theta) }^{2} } \\ \\ \\ = \frac{{ \cos( \theta) }^{2} }{ { \cos( \theta) }^{2} } \\ \\ \\ = 1$

= RHS (HENCE PROVED)

Points should be kept in Mind :-

1. At the time of simplifying the Trigonometric ratios we should try to bring them in the form cos and sin. It is the base of all trigonometric ratios and easy to handle & operate.

2.We should remember all the Trigonometric identities and algebraic identities so to perform simplifications.

3. At the time of simplifying we shouldn't get confused and lost the path rather first we should analyse and plan then apply the steps.

Answer 2

this is the answer.

please mark this as the brainliest answer