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# P2 Pure Maths further trig watch

1. Sin 10 + sin 50 = sin 70

Prove this without the use of calc or tables
Sin 10 + sin 50 = sin 70

Prove this without the use of calc or tables
We have: sin(A+B)+sin(A-B)=[SinAcosB+cosAsinB]+[sinAcosB-cosAsinB]=2sinAcosB

A+B=50, A-B=10
A=30, B=20.

sin10+sin50=2sin30cos20
sin10+sin50=2[1/2]cos(90-70)
sin10+sin50=sin70 [as cos(90-x)=sinx]

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