$\frac{4}{3}$

$\frac{49}{41}$

$\frac{4}{5}$

$\frac{41}{49}$

1st quadrant

2 nd quadrant

3rd quadrant

4th quadrant

$\sin 10 \theta+\sin 7 \theta-\sin 3 \theta$

$\sin 10 \theta+\sin 7 \theta-\sin 5 \theta$

$\sin 10 \theta+\sin 7 \theta+\sin 3 \theta$

$\sin 10 \theta+\sin 7 \theta+\sin 5 \theta$

$4 \operatorname{cosech} 2 x \tanh 2 x$

$4 \operatorname{sech} 2 x \operatorname{coth} 2 x$

$4 \operatorname{sech} 2 x \tanh 2 x$

$4 \cosh 2 x(\operatorname{cosech} 2 x)^2$