Question

prove that (sinA/1-сosA--1-cosA/sinA)×
(cos A/1-sin A-1-sinA/cos A)=4​

Answer 1

Step-by-step explanation:

[sin²A-(1-cosA)²/sinA(1-cosA)] [cos²A-(1-sinA)²/cosA(1-sinA)]

=[sin²A-1+2cosA-cos²A/sinA(1-cosA)] [cos²A-1+2sinA-sin²A/cosA(1-sinA)]

=[sin²A-(sin²A+cos²A)+2cosA-cos²A/ sinA(1-cosA)][cos²A-(sin²A+cos²A)+2sinA-sin²A/cosA(1-sinA)]

=[2cosA-2cos²A/sinA(1-cosA)] [2sinA-2sin²A/cosA(1-sinA)]

=[2cosA(1-cosA)/sinA(1-cosA)] [2sinA(1-sinA)/cosA(1-sinA)]

=(2cosA/sinA)(2sinA/cosA)

=2tanA×2cotA

=4tanAcotA

=4