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| 1. |
Sec8x-1/sec4x-1=tan8x/tan2x.. Prove |
| Answer» L.H.S.={(1-cos8x)×cos4x}/{(1-cos4x)×cos8x}={(1-(1-2sin^2 4x))×cos4x}/{(1-(1-2sin^2 2x))×cos8x}={(2sin^2 4x)×cos4x}/{(2sin^2 2x)×cos8x}={(2sin4x cos4x)×sin4x}/{(2sin^2 2x)× cos4x}={(sin8x)×sin4x}/{(2sin^2 2x)×cos8x}={tan8x×(2sin2x cos2x)/{2sin^2 2x}={tan8x}/{sin2x/cos2x}={tan8x}/{tan2x}=R.H.S. | |