Question

(1 + cot A - cosec A) (1 + tan A + sec A) = 2​

Answer 1

Answer:

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Step-by-step explanation:

(1+cot A-cosec A).(1+tanA+secA)= 2

L.H.S.

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

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

=[(sinA+cosA)^2-(1)^2]/sinA.cosA.

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

=( 1+2.sinA.cosA -1)/sinA.cosA.

= 2.sinA.cosA/sinA.cosA

= 2 , proved.

Answer 2

Answer:

(1+cotA-cosecA)(1+tanA+secA)

={1(1+tanA+secA)+cotA (1+tanA+secA) -cosecA (1+tanA+secA)

=1+tanA+secA+cotA+1+cosecA-cosecA-secA

-sec.cosec

=2+tanA+cotA-secA.cosecA

=2+(sinA/cosA)+(cosA/sinA)-(1/sinA.cosA)

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

=(2sinA.cosA+1-1)/(sinA.cosA)

={2(sinA.cosA)/(sinA.cosA)}

=2