162 Higher Engineering Mathematics
5. cos A sin B =
1
2
[sin(A + B) − sin(A − B)]
⎡
⎢
⎣
cosh θ cosh φ =
1
2
[sinh(θ + φ)
− sinh(θ − φ)]
⎤
⎥
⎦
6. sin
3 A =
3
4
sin A −
1
4
sin 3 A
sinh 3 θ =
1
4
sinh 3θ −
3
4
sinh θ
7. cot 2 A(sec 2 A − 1) =1
[coth 2 θ(1 − sech 2 θ) = 1]
5. cos A sin B =
1
2
[sin(A + B) − sin(A − B)]
⎡
⎢
⎣
cosh θ cosh φ =
1
2
[sinh(θ + φ)
− sinh(θ − φ)]
⎤
⎥
⎦
6. sin
3 A =
3
4
sin A −
1
4
sin 3 A
sinh 3 θ =
1
4
sinh 3θ −
3
4
sinh θ
7. cot 2 A(sec 2 A − 1) =1
[coth 2 θ(1 − sech 2 θ) = 1]