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Prove the identity: sec® =tan®6 +3 छा 0 56८ 0 को. |
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Answer» tan^6A + 3tan^2A.sec^2A + 1 = tan^6A + 3tan^2A(1+ tan^2A ) + 1 [since sec^2A = 1+ tan^2A] = tan^6A + 3tan^4A + 3 tan^2A + 1 = (tan^2A)^3+ 3(tan^2A)^2+ 3 (tan^2A) + 1It is in the form of a^3+ 3a^2b + 3ab^2+b^3= (a + b)^3∴ (tan^2A)^3+ 3(tan^2A)^2+ 3 (tan^2A) + 1 = (tan^2A + 1)^3 = (sec^2A)^3 = sec^6A |
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