The value of sin² 30 – sin² 40 + sin² 45 – sin² 55 – sin² 35 + sin² 45 – sin² 50 + sin² 60 is:

Options
a) 4
b) 0
c) 1
d) 2

Solution

As per question

sin² 30 – sin² 40 + sin² 45 – sin² 55 – sin² 35 + sin² 45 – sin² 50 + sin² 60
sin² 30 + sin² 60 + sin² 45 + sin² 45 – sin² 40 – sin² 50 – sin² 55 – sin² 35
sin² 30 +(sin 90-30)² + sin² 45 + (sin 90-45)² – sin² 40 – (sin 90-40)² – sin² 55 – (sin 90-55)²
Formula :- sin ( 90 – =
sin² 30 +cos² 30 + sin² 45 + cos² 45 – (sin² 40 + cos² 40) – (sin² 55 + cos² 55)
Formula:
1 + 1 – (1) – (1) = 0

Ans is ) 0