(1 + cot A - cosec A) (1 + tan A + sec A) = 2
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Answered by
3
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.
Answered by
1
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
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