Using the trigonometric identity (sinx)^2 + (cosx)^2 = 1, show that (secx)^2 = (tanx)^2 + 1 is also a trigonometric identity.
We can divide by (cosx)^2 across the identity (sinx)^2 + (cosx)^2 = 1 (which can be derived from properties of the unit circle and a bit of Pythagoras’ theorem) to achieve
[(sinx)^2 / (cosx)^2] + [(cosx)^2 / (cosx)^2] = [1 / (cosx)^2]
Which leaves us with our desired identity
(tanx)^2 + 1 (secx)^2 = 1
AB
Related Maths A Level answers
All answers ▸Integrate the function xsin(4x^2) with respect to x, using the integration by substitution method.
Find the equation of the tangent to the curve y = 3x^2 + 4 at x = 2 in the form y = mx + c
Find the inverse of a 2x2 matrix
find the coordinate of the maximum value of the function f(x) = 9 – (x – 2)^2