Question

If sinA+cosA=m and secA+cosecA=n then find the value of n(m+1)(m-1).

Answer 1

Step-by-step explanation:

LHS:

n(m2- 1)

= secA +cosecA [ (sinA +cosA)2- 1]

= secA + cosecA [ sin2A + cos2A + 2 sinA.cosA -1]

= secA +cosecA [ 1 +2 sinA.cosA -1] [sin2A +cos2A =1]

= secA +cosecA [ 2sinA cosA]

= 2 secA sinA cosA + 2 cosecA sinA cosA

= 2sinA + 2 cosA [secA*cosA=1 and cosecA*sinA=1]

= 2(sinA +cosA)

= 2 m [sinA +cosA =m]

= RHS

Answer 2

Answer:

= 2m

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