Given:
Given that a trigonometric statements.
Required:
To check whether the given statements are true or false.
Explanation:
(A)
[tex]\sin67\degree=\sin(42\degree+25\degree)[/tex]Now, by using the formula
[tex]\sin(42\degree+25\degree)=\sin42\degree\cos25\degree+\cos42\degree\sin25\degree[/tex]Therefore, the option A is true.
(B)
[tex]\tan(67)=\tan(70-3)[/tex]Now, by using the formula,
[tex]\tan(70-3)=\frac{\tan70-\tan3}{1+\tan70\tan3}[/tex]Therefore, the option B is false.
(C)
[tex]\cos67=\cos(41+26)[/tex]Now, by using the formula
[tex]\cos(41+26)=\cos41\cos26+\sin41\sin26[/tex]Therefore, the option C is true.
(D)
[tex]\tan67=\tan(23+44)[/tex]Now by using the formula,
[tex]\tan(23+44)=\frac{\tan23+\tan44}{1-\tan23.\tan44}[/tex]Therefore, the option D is true.
(E)
[tex]\sin67=\sin(81-14)[/tex]Now, by using the formula
[tex]\sin(81-14)=\sin81\cos14-\cos81\sin14[/tex]Therefore, the option E is false.'
Final Answer:
The true statements are option A, C, and D.