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Trigonometric identities

If you would please give me each step to solve these problems so I can get a better understanding how to solve these types of problems would be very helpful. Thanks.

Graph each expression and use the graph to conjecture an identity. Then verify your conjecture algebraically.

1. sec x - sin x tan x

Verify that each equation is an identity.

1. tan^2 x - sin^2 x = (tan x sin x)^2

Solution Preview

sec(x) - sin(x). tan(x)
= 1/cos(x) - sin(x).sin(x)/cos(x)
= {1 - sin^2(x)}/cos(x)
= cos^2(x)/cos(x) = cos(x) ...

Solution Summary

This shows how to graph and verify trigonometric identities.