a. Use you calculator to determine which two of the followingequations is an identity. 1/(sinx + cosx)= cscx +secx 1/(1-sin^2x)= 1+ tan^2x b. Verify the identity equation.

Question

a. Use you calculator to determine which two of the following equations is an identity.

1 / (\sin x + \cos x) = \csc x + \sec x

1 / (1 - \sin^{2} x) = 1 + \tan^{2} x

b. Verify the identity equation.

Answer 1

b)

1 / (\sin x + \cos x) = \csc x + \sec x = 1 / (\sin x + \cos x) = 1 / \sin x + 1 / \cos x

not true

1 / (1 - \sin^{2} x) = 1 + \tan^{2} x (1 - \sin^{2} x = \cos^{2} x) s o : 1 / \cos^{2} x = 1 + \sin^{2} x / \cos^{2} x \Rightarrow 1 / \cos^{2} x = (\cos^{2} x + \sin^{2} x) / \cos^{2} x a n d (\cos^{2} x + \sin^{2} x = 1) 1 / \cos^{2} x = 1 / \cos^{2} x

Answer 2

1 / (\sin x + \cos x) = \csc x + \sec x

\csc x = 1 / \sin x

\sec x = 1 / \cos x

1 / (\sin x + \cos x) = 1 / \sin x + 1 / \cos x

not true

1 / (1 - \sin^{2} x) = 1 + \tan^{2} x

1 - \sin^{2} x = \cos^{2} x

1 + \tan^{2} x = \sec^{2} x

1 / \cos^{2} x = \sec^{2} x

\sec^{2} x = \sec^{2} x

Answers (2)