Question

(cosecA-sinA).(secA-cosA).(tanA+citA)=1​

Answer 1

Answer:

LHS - (cosecA - sinA).(secA - cosA).(tanA + cotA)

= (1/sinA - sinA).(1/cosA - cosA).(sinA/cosA + cosA/sinA). (since- cosecA= 1/sinA , secA = 1/cosA , tanA = sinA/cosA and cotA = cosA/sinA)

=(1-sin^2A/sinA).(1-cos^2A/cosA).(sin^2A+cos^2A/sinA.cosA). (take LCM)

= (cos^2A/sinA).(sin^2A/cosA).(sin^2A+cos^2A/cosAsinA)

= (cos^2A/sinA).(sin^2A/cosA).(1/sinA+CosA). (since- sin^2A + cos^2A = 1)

= (cos^2A.sin^2A/sin^2Acos^2A).

=1= RHS