Question

(sinA + cosecA)2 + (cosA + secA)

2 = 5 + sec2A . cosec2A​

Answer 1

Answer:

(sinA + cosecA)2 + (cosA + secA) 2 = 5 + sec2A . cosec2A​

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Step-by-step explanation :-

L.H.S

(sinA + cosecA)2 (it is in the form of (a+b)2) So, sinA=a and cosecA=b

= sin2A+cosec2A +2*sinA*cosecA       [ sinA*cosecA=1] so,

= sin2A+cosec2A +2  ⇒ 1st equation

(cosA + secA) 2 (it is in the form of (a+b)2) so, cosA=a and secA=b

= cos2A+sec2A+2*cosA*secA       [cosA*secA=1] so,

= cos2A+sec2A+2 ⇒ 2nd equation

1 and 2 equations

= sin2A+cosec2A +2 = cos2A+sec2A+2   [sin2A+cos2A =1] so,

= 2+2+1+ cosec2A . sec2A

= 5 + sec2A . cosec2A​

hope it helps