Question

If sec theta=x+1/4x then prove that sec theta+tan theta=2x or 1/2x

Answer 1

Answer:

We have sec theta = x +1/4x

Now square both sides

Sec square theta =(x+1/4x)^2

=x^2+1/16x^2+1/2

Now subtract 1 both the sides to get tan theta

Sec square theta-1=x^2 +1/16x^2 +1/2-1

=x^2 +1/16x^2-1/2, this is the formula for (x-1/4x)^2

Tan square theta =(x-1/4x)^2

Tan theta =+-(x-1/4x)

Now there are 2 values of tan theta,x-1/4x and -x+1/4x put each of them in the situation sec theta + tan theta you will get your answers as 2x or 1/2x

Hope this help.