Question

show that ( 1 + sinA/cosA × sinB/cosB) ² + ( sinA/cosA - sinB/cosB) ² = 1/cos²A.cos²B



pls answer fast​

Answer 1

Step-by-step explanation:

Firstly, note that (1+(sinAsinB)/(cosAcosB))=(cosAcosB+sinAsinB)/(cosAcosB)

                                                                    =cos(A-B)/(cosAcosB)

Also, ( sinA/cosA - sinB/cosB)=(sinAcosB-sinBcosA)/(cosAcosB)

                                                =sin(A-B)/(cosAcosB)

Square both equations and add:

(sin^2 (A-B)+cos^2 (A-B))/cos^2 A cos^2 B=1/cos²A.cos²B as required on using the identity sin^2 x +cos^2 x =1.

Generally, my advice with these sorts of problems is to jump right in.

Answer 2

Step-by-step explanation:

it was easy. i hope its not difficult to understand my writing.

i hope its helpful.

good luck.