CBSE BOARD X, asked by aberoshan533, 10 months ago

If sec A = x + 1/4x, prove that sec A + tan A = 2x or 1/2x

Answers

Answered by SaiKarthik09
2

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

Answered by orjit
2

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:

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