Question

Cosec 4A + cosec 8A + cosec 16 A = cot 2A-cot 16.​

Answer 1

Step-by-step explanation:

Cosec2A+Cosec4A+Cosec8A

1/sin2A+1/sin4A+1/Sin8A. i.e (we know sinx = 1/cosecx )

1/sin2A+1/2sin2A.cos2A+1/2sin4A.cos4A

1/sin2A+1/2sin2A.cos2A+1/2sin2Acos2A.cos4A

(1/sin2A)[1++1/2cos2A+1/cos2A.cos4A]

(1/sin2A)[cos4Acos2A+cos4A+1]/cos2Acos4A

(1/sin2A)[cos4Acos2A+2cos^2 2A-1+1]/cos2Acos4A

(1/sin2A)[cos4Acos2A+2cos^2 2A]/cos2Acos4A

(Cos2A)[cos4A+2cos2A]/cos4ASin2A

(Cos2A)[2cos^2 2A-1+2cos2A]/cos4ASin2A

Cot2A [2Cos2A (cos2A+1)-1]/cos4A

=R.H.S

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