Prove that tan^2(x)=1/(cos^2(x))-1

tan^2(x)=1/(cos^2(x))-1 Left hand side of the equation (LHS)=tan^2(x) Use the identity tan(x)=sin(x)/cos(x) and substitute it into the LHS LHS=sin^2(x)/cos^2(x) Use the identity sin^2(x)+cos^2(x)=1 and rearrange to make sin^2(x) the subject sin^2(x)=1-cos^2(x) Substitute this into the LHS: sin^2(x)/cos^2(x)=1-cos^2(x)/cos^2(x) Simplify this to give the RHS of the equation given:1-cos^2(x)/cos^2(x)=1/(cos^2(x))-1 Therefore the LHS=RHS

PA
Answered by Phoebe A. Further Mathematics tutor

2285 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

Use differentiation to show the function f(x)=2x^3–12x^2+25x–11 is an increasing function for all values of x


How would I solve the following equation d^2x/dt^2 + 5dx/dt + 6x = 0


If the equation of a curve is x^2 + 9x + 8 = y, then differentiate it.


How do I determine if a stationary point on a curve is the maximum or minimum?


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