Question

Prove that sin43•cos47•+cos43•sin47•=1

Answer 1

sin43 × cos47 + cos43 × sin47

= sin43 × sin(90-47) + cos43 × cos(90-47) --- (1)

= sin43 × sin43 + cos43 × cos43

= (sin4 3)^2 + (cos43)^2

= 1 -------- (2)

Formulas used in

1) sinA = cos(90-A)

2) (sinA)^2 + (cosA)^2 = 1

Answer 2

LHS=sin43.sin(90-47)+cos43.cos(90-47)

      =sin43.sin43+cos43.cos43

      =sin^2 43+cos^2 43(sin^2 a+cos^2 a=1)

       =1

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