Taking 0 = 30°, verify each of the following:
(i) sin 2 theta = 2 sin theta cos theta
(ii) cos 2 theta = 2 cos square theta-1 = 1-2 sin square theta
(iii) tan 2 theta = 2tan theta/1-tan square theta
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Answer:
let the 2theta be A+B
then
sin(A+B)=SinA CosB+CasAsinB
since A&B are same
so
Sin A+A =SinACosA+CosASinA
then
Sin 2thet=Sin2A=2SinACosA
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