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Question

Question: \({\sin h}3z\) equals....

sin⁡h3z{\sin h}3z equals.

A

3sinh⁡z−4sinh⁡3z3\sinh z - 4\sinh^{3}z

B

4sin⁡h3z−3sin⁡hz4{\sin h}^{3}z - 3{\sin h}z

C

3sin⁡hz+4sin⁡h3z3{\sin h}z + 4{\sin h}^{3}z

D

None of these

Answer

3sin⁡hz+4sin⁡h3z3{\sin h}z + 4{\sin h}^{3}z

Explanation

Solution

sinh⁡3z=−isin⁡3(iz)=−i[3sin⁡(iz)−4sin⁡3(iz)]\sinh 3z = - i\sin 3(iz) = - i\lbrack 3\sin(iz) - 4\sin^{3}(iz)\rbrack

=−i[3isinh⁡z−4i3sinh⁡3z]=3sin⁡hz+4sin⁡h3z= - i\lbrack 3i\sinh z - 4i^{3}\sinh^{3}z\rbrack = 3{\sin h}z + 4{\sin h}^{3}z.