sec6A-tan6A= 1+3tan2A+3tan4A
siddhartharao77:
Is it tan 2a (or)tan^2a?
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Given LHS = sec^6 A - tan^6 A.
W.K.T a^3 - b^3 = (a - b)(a^2 + ab + b^2)
= (sec^2 A - tan^2 A)((sec^2 A)^2 + sec^2 A tan^2 A + tan^ 4A)
W.K.T sec^2 theta = 1 + tan^2 theta (or) sec^2 theta - tan^2 theta = 1.
= (1)((sec ^2A)^2 + (1 + tan^2 A)(tan^2 A) + (tan^4 A)
= (sec^2 A)^2 + (1 + tan^2 A)(tan^2 A) + (tan^4 A)
= (1 + tan^2 A)^2 + (1 + tan^2 A)(tan^2 A) + (tan^4 A)
= (1 + tan^2 A)[(1 + tan^2 A) + tan^2 A] + tan^4 A
= (1 + tan^2 A)(1 + 2 tan^2 A) + tan^4 A
= 1 + 2tan^2 A + tan^2 A + 2 tan^4 A + tan^4 A
= 1 + 3 tan^2 A + 3 tan^4 A
LHS = RHS.
Hope this helps!
W.K.T a^3 - b^3 = (a - b)(a^2 + ab + b^2)
= (sec^2 A - tan^2 A)((sec^2 A)^2 + sec^2 A tan^2 A + tan^ 4A)
W.K.T sec^2 theta = 1 + tan^2 theta (or) sec^2 theta - tan^2 theta = 1.
= (1)((sec ^2A)^2 + (1 + tan^2 A)(tan^2 A) + (tan^4 A)
= (sec^2 A)^2 + (1 + tan^2 A)(tan^2 A) + (tan^4 A)
= (1 + tan^2 A)^2 + (1 + tan^2 A)(tan^2 A) + (tan^4 A)
= (1 + tan^2 A)[(1 + tan^2 A) + tan^2 A] + tan^4 A
= (1 + tan^2 A)(1 + 2 tan^2 A) + tan^4 A
= 1 + 2tan^2 A + tan^2 A + 2 tan^4 A + tan^4 A
= 1 + 3 tan^2 A + 3 tan^4 A
LHS = RHS.
Hope this helps!
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