Question

Prove that sin 43 cos47 + sin47 cos43=1

Answer 1

Answer:

This is the answer thank you

Answer 2

Step-by-step explanation:

To prove: sin 43 cos47 + sin 47 cos 43 = 1

L.H.S:

sin 43 cos47 + sin 47 cos 43

Multiplying '2' in the numerator and denominator:

= $\frac{1}{2}$ $2(sin 43 cos47 + sin 47 cos 43)$

= $\frac{1}{2}$$(2sin 43 cos47 + 2sin 47 cos 43)$                   [2sinA cosB =sin(A+B) + sin(A-B)]

=$\frac{1}{2}$$(sin (43+47) + sin (43-47) + sin(47+43) +sin (47-43))$  

=$\frac{1}{2}(sin(90) + sin(-4) + sin (90) + sin (4))$

=$\frac{1}{2} (sin90) - sin(4) + sin(90) + sin (4))$

=$\frac{1}{2} (2)$

=1

=R.H.S.

Hence proved