Question

The Value
of cos² 45° - sin^2 15 is?​

Answer 1

Answer:

Step-by-step explanation:

cos245∘−sin215∘  

=cos245∘−sin2(45∘−30∘)(LHS)

We know that  sin(A−B)=sinA⋅cosB−cosA⋅sinB  

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.