Question

Write the following in their simplest form, involving only one trigonometric function:

tanA/sec^2A -2

Answer 1

\[\frac{ \tan \theta }{ \sec ^2\theta-2 }\]

Answer 2

\[\large={\sin A \over \cos A} \times{1\over {1\over \cos^2A}-2}\]

Answer 3

\[={\sin A \over \cos A} \times{\cos^2 A \over 1-2\cos^2 A}\]

Answer 4

\[={\sin A \times \cos A \over 1-2\cos^2 A}\]

Answer 5

next using the identities: \[\sin(2x)=2\sin x \cdot \cos x\]\[\cos(2x)=2\cos^2x-1\]

we get:\[\large{={\frac12\sin \left( 2A \right)\over -\left( \cos \left( 2A \right) \right)}\\=\color{green}{-\frac12\tan \left( 2A \right)}}\]