Question #498a1

2 Answers
Nov 6, 2017

Proof

Explanation:

(cotx + tanx) / cotx = sec^2(x)

Convert tan(x) and cot(x) in terms of sin and cos

(cos(x)/sin(x)+sin(x)/cos(x))/(cos(x)/sin(x))

Take the LCD on the numerator and apply

((sin^2(x)+cos^2(x))/(sin(x)cos(x)))/(cos(x)/sin(x))

Apply algebra

((sin^2(x)+cos^2(x))/(cancel(sin(x))cos(x)))x (cancel(sin(x))/cos(x))

((sin^2(x)+cos^2(x))/(cos^2(x)))

Apply trigonometric identity

color(red)(sin^2(x)+cos^2(x)=1

1/cos^2(x) root=sec^2(x)

Nov 6, 2017

Please refer to a Proof given in the Explanation.

Explanation:

We have,

(cotx+tanx)/cotx,

=cotx/cotx+tanx/cotx,

=1+tanx*tanx..........[because, 1/cotx=tanx],

=1+tan^2x,

=sec^2x.