Question

Sin85-sin25-cos55=?

Answer 1

$\huge\bold{Answer}$

$sin85 - sin25 - cos55$

$2(cos \frac{85 + 25}{2} )(sin \frac{85 - 25}{2} ) - cos55$

$2cos( \frac{110}{2} )sin( \frac{60}{2} ) - cos55$

$2.cos55.sin30 - cos55$

By taking " $\bf\pink{cos55}$ " as common.

$cos55(2sin30 - 1)$

$cos55(2 \times ( \frac{1}{2} ) - 1)$

$cos55 \times (0) = 0$

$\bf\red{Identity\:used:-}$

$\bf\boxed{sinC-SinD=2.(cos\frac{C+D}{2}).(sin\frac{C-D}{2})}$