Question

Prove that:-
Cos A - Sin A + 1/Cos A + Sin A - 1 = 1/Cosec A - Cot A​

Answer 1

Secondary School Math 8+4 pts

Cos A- sin A+1/cos A+ sin A-1=cosec A+cot A

Report by Sweenaanerig 15.09.2016

Answers

ARoy

ARoy★ Brainly Teacher ★

cosA-sinA+1/cosA+sinA-1

=(cosA-sinA+1)(cosA+sinA+1)/(cosA+sinA-1)(cosA+sinA+1)

=(cos²A-cosAsinA+cosA+cosAsinA-sin²A+sinA+cosA-sinA+1)/{(cosA+sinA)²-(1)²}

=(cos²A-sin²A+2cosA+1)/(cos²A+2cosAsinA+sin²A-1)

={cos²A+2cosA+(1-sin²A)}/(1+2cosAsinA-1) [∵, sin²A+cos²A=1]

=(cos²A+2cosA+cos²A)/2cosAsinA

=(2cos²A+2cosA)/2cosAsinA

=2cosA(cosA+1)/2cosAsinA

=(cosA+1)/sinA

=cosA/sinA+1/sinA

=cotA+cosecA

=cosecA+cotA (Proved)