If sec A = x + 1/4x then prove that tan A + secA = 2x or 1/2x
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Answered by
6
heya it's Aastha...
◆Taking LHS...
Sec A = x + 1/4x
Tan A = √[(Sec2 A) - 1]
= √[(x + 1/4x)2 - 1]
= √[(x2 + 1/16x2 + 1/2) - 1]
= √[x2 + 1/16x2 - 1/2]
= √[(x - 1/4x)2]
= (x - 1/4x)
Sec A + Tan A = (x + 1/4x) + (x - 1/4x)
= 2x
LHS =RHS
hence proved...
◆Taking LHS...
Sec A = x + 1/4x
Tan A = √[(Sec2 A) - 1]
= √[(x + 1/4x)2 - 1]
= √[(x2 + 1/16x2 + 1/2) - 1]
= √[x2 + 1/16x2 - 1/2]
= √[(x - 1/4x)2]
= (x - 1/4x)
Sec A + Tan A = (x + 1/4x) + (x - 1/4x)
= 2x
LHS =RHS
hence proved...
Answered by
2
yes this is the right answer
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