Question

prove that
sin²45°-sin²15°=√3/4​

Answer 1

Answer:

=3‾√4=RHS.

Step-by-step explanation:

cos245∘−sin215∘

=cos245∘−sin2(45∘−30∘)(LHS)

We know that sin(−)=⋅−⋅

Therefore, LHS =cos245∘−(sin45∘⋅cos30∘−cos45∘⋅sin30∘)2

=12−(12‾√×3‾√2−12‾√×12)2

=12−(3‾√22‾√−122‾√)2

=12−(3‾√−122‾√)

= 12−((3‾√−1)28)

=12−(3‾√−1)28

=12−4−23‾√8

=12−2−3‾√4

=2−(2+3‾√)4

=3‾√4=RHS.

Hence, the problem is solved.