Question

prove that sin33+cos65=cos3​

Answer 1

Answer:

$sin(90 - 57) + cos65 \\ = cos57 + cos65 \\ = 2cos( \frac{57 + 65}{2} )cos( \frac{65 - 57}{2} ) \\ = 2cos61cos4$

Answer 2

Step-by-step explanation:

Sin 33 + cos 63= cos 3

LHS = Sin 33 + Cos 63

Sin 33 = Sin (30+3)

Cos 63 = Cos (60+3)

Sin (A+B) = SinA Cos B + CosA Sin B

Cos (A+B) =CosA Cos B - SinA - Sin B

=Sin 30 Cos 30 + Cos 60 Cos 3 + Cos 30 Sin 3-Sin 60 Sin 3

As we know that Cos α = Sin (90-α)

=> Cos 60 = Sin 30 & Cos = Sin 60

= Sin 30 Cos 3 + Sin 30 Cos 3 + Sin 60 Sin 3 Sin 60 Sin 3

= 2 Sin 30 Cos 3

= Sin 30 1/2

=> 2 Sin 30 = 1

= Cos 3

= RHS