Given that sin(x)^2 + cos(x)^2 = 1, show that sec(x)^2 - tan(x)^2 = 1 (2 marks). Hence solve for x: tan(x)^2 + cos(x) = 1, x ≠ (2n + 1)π and -2π < x =< 2π(3 marks)

sin(x)2 + cos(x)2 = 1

Dividing by cos(x)2 gives:

tan(x)2 + 1 = sec(x)2 

Which rearranges as:

sec(x)2 - tan(x)2 = 1 as required.

tan(x)2 + cos(x)2 = 1

sec(x)2 - 1 + cos(x)2 = 1

sec(x)2 + cos(x)2 = 2

1 + cos(x)4 = 2cos(x)2

(cos(x)2 -1)2 = 0

cos(x)2 = 1

cos(x) = 1

x = 0, 2π

AR
Answered by Alistair R. Maths tutor

3732 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

You are given the equation of the line y=x^3+x^2-2x. Find the stationary points of the curve and determine the maximum and minimum points and find where it crosses the x-axis and thus sketch the graph


Points A and B have coordinates (–2, 1) and (3, 4) respectively. Find the equation of the perpendicular bisector of AB and show that it may be written as 5x +3 y = 10.


A curve has the equation (x+y)^2 = xy^2. Find the gradient of the curve at the point where x=1


If a circle passes through points (2,0) and (10,0) and it has tangent line along the y-axis, then what are the possible equations of the circle?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning