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Pythagorean Properties
Co-functions
Double Argument Properties
100
Express \[1 - {\cos ^2}x\] in terms of one trig function.
\[{\sin ^2}x\]
100
Express \[\sin \left( {\frac{\pi }{2} - x} \right)\] as the trig function of a single argument.
\[\cos x\]
100
Express \[\cos (A - B)\] using only single argument(s) A and/or B.
\[\cos A\cos B + \sin A\sin B\]
200

Give a Pythagorean Trig Property that contains secant.

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

200
Express \[\cot x\]using its co-function.
\[\tan \left( {\frac{\pi }{2} - x} \right)\]
200
Express \[\sin (A + B)\] using only single argument(s) A and/or B.
\[\sin A\cos B + \cos A\sin B\]
300
Simplify: \[{\csc ^2}x - {\cot ^2}x\]
1
300
\[Arc\cos \left[ {\sin \left( {{{34}^ \circ }} \right)} \right]\]
\[{56^ \circ }\]
300
Express \[\tan (A - B)\] using only the tangent function of single argument(s) A and/or B.
\[\frac{{\tan A - \tan B}}{{1 + \tan A\tan B}}\]
400
Simplify: \[{\tan ^2}x - {\sec ^2}x\]
-1
400
\[Arc\cot \left[ {\tan \left( {\frac{\pi }{6}} \right)} \right]\]
\[\frac{\pi }{3}\]
400
Find the exact value of \[\sin ({75^ \circ })\]
\[\frac{{\sqrt 2 + \sqrt 6 }}{4}\]
500
Express \[{\tan ^2}x - {\sec ^2}x + {\sin ^2}x\] using only one trigonometric function.
\[ - {\cos ^2}x\]
500
\[Arc\sec \left[ {\csc \left( {{{17.9}^ \circ }} \right)} \right]\]
\[{72.1^ \circ }\]
500
Find the exact value of \[\cos \left( {{{105}^ \circ }^{}} \right)\]
\[ - \frac{{\sqrt 6 - \sqrt 2 }}{4}\]