If sec theta=x +1/4x, find the value of sec theta+ tan theta.......
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harshkumar88999:
2x
is the ans.
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1 + tan^2 m = sec^2 m, or
tan^2 m = sec^2 m -1 = [x + 1/(4x)]^2 -1
= x^2 + (1/2) + 1/(16x^2) - 1
= x^2 - (1/2) + 1/(16x^2)
= [x - 1/(4x)]^2, or
tan m = x - 1/(4x) or -[x - 1/(4x)]
Therefore sec m + tan m = x + 1/(4x) + x - 1/(4x) = 2x. Proved
Alternatively, sec m + tan m = x + 1/(4x) - x + 1/(4x) = 2/(4x) = 1/(2x)
tan^2 m = sec^2 m -1 = [x + 1/(4x)]^2 -1
= x^2 + (1/2) + 1/(16x^2) - 1
= x^2 - (1/2) + 1/(16x^2)
= [x - 1/(4x)]^2, or
tan m = x - 1/(4x) or -[x - 1/(4x)]
Therefore sec m + tan m = x + 1/(4x) + x - 1/(4x) = 2x. Proved
Alternatively, sec m + tan m = x + 1/(4x) - x + 1/(4x) = 2/(4x) = 1/(2x)
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