Question

40.
sin47°+sin610-sin11-sin25°
170
B) cos7°
C)​

Answer 1

Answer:

B) cos 7∘

Step-by-step explanation:

sin47∘−sin25∘+sin61∘−sin11∘

Using the formula for sinc−sind= 2cos(c+d)/2 - sin(c−d)/2

=2cos(47+25)/2∘sin(47−25)/2∘ +2cos(61+11)/2∘sin(61−11)/2∘

=2cos36∘sin11∘+2cos36∘sin25∘

=2cos36∘(sin11∘+sin25∘)

=2cos36∘(sin25∘+sin11∘)

Using sinc+sind=2sin(c+d)/2 - cos(c−d)/2

=2cos36∘[2sin(25+11)/2∘cos(25−11)/2∘]

=4cos36∘sin18∘cos7∘

cos36∘= $\frac{ \sqrt{5} + 1}{4}$

sin18= $\frac{ \sqrt{5} - 1}{4}$

=4×(5−1)/(4×4)cos7∘

=cos7∘