Question

cosec theta ( 1+ cos theta) (cosec theta - cot theta) = 1

Answer 1

If you have any doubts then contact....

Answer 2

Concept:

Trigonometry is the basic concept of Mathematics. It helps not only finding out the algebraic problems but also helps in Mathematical numericals of Geography and Physics.

Given:

The following expression is given

$\csc( \alpha ) (1 + \cos( \alpha ) )( \csc( \alpha ) - \cot( \alpha ) ) = 1$

Find:

Prove that LHS is equal to RHS.

Solution:

Applying the Trigonometric Formulas we get, First solving the LHS we get,

$\frac{1}{ \sin \alpha } (1 + \cos\alpha)( \frac{1}{ \sin \alpha } - \frac{ \cos\alpha }{ \sin\alpha} ) \\ (\frac{1 + \cos \alpha }{ \sin\alpha} )( \frac{1 - \cos \alpha }{ \sin\alpha } ) \\ \frac{1 - { \cos }^{2} \alpha }{ \sin^{2} \alpha } \\ \frac{\sin^{2} \alpha}{\sin^{2} \alpha} \\ 1$

and RHS is equal to

$1$

therefore LHS is equal to RHS.

Hence Proved, that LHS is equal to RHS.

#SPJ2