If sec A = x + 1/4x, prove that sec A + tan A = 2x or 1/2x
Answers
Answer:
Explanation:tan^2(A)=sec^2(A)-1
=(x+1/4x)^2-1
x^2+1/16x^2+1/2-1
x^2+1/16x^2-1/2=(x-1/4x)^2
Tan^2(A)=(x-1/4x)^2
TanA=+(or)-(x-1/4x)
secA+TanA=x+1/4x+x-1/4x=2x
secA+tanA=x+1/4x+(-x+1/4x)=1/2x
Answer: sec a = 1/x + 1/4x
we know that , 1 + tan2a = sec2a (2 is in form of square)
putting value of sec a in above equation
tan2a = (x + 1/4x)2 - 1
tan2a = x2 + 1/16x2 + 1/2 - 1
tan2a = (x- 1/4x)2
tan a = (x-1/4x) or -(x-1/4x)
when,tan a is = x-1/4x sec a + tan a = x+1/4x + x+1/4x = 2x
when,tan a is = -(x-1/4x) sec a + tan a = x +1/4x - x + 1/4x
= 1/4x + 1/4x
= 2/4x
= 1/2x
hence prooved.
Explanation: