Question

Prove the following.
sec theta (1-sin theta) (sec theta+tan theta)=1​

Answer 1

i hope. u understand

..the concept of trigonometry function

Answer 2

Answer:

Step-by-step explanation:

secФ ( 1 - sinФ ) ( secФ + tanФ ) = 1

L.H.S

 =  secФ ( 1 - sinФ ) ( secФ + tanФ )

= ( secФ - sinФ secФ) ( secФ + tanФ )

As we know    secФ = 1/cosФ

Therefore,  

= ( 1/cosФ - sinФ*1/cosФ) ( secФ + tanФ )  

As we know   tanФ =  sinФ/cosФ

Therefore,  

=   ( secФ - tanФ )( secФ + tanФ )

=  sec^2Ф - tan^2Ф

= 1    (R.H.S)

[Using the trigonometry identity        

               sec^2Ф = 1 + tan^2Ф

            sec^2Ф - tan^2Ф = 1 ]