213)
i)Prove that cos2A + cos2(A+ pie/3) + cos2(A- pie/3) = 3/2
ii)If sin4x/a + cos4x/b = 1/(a+b),Prove that sin12x/a5 + cos12x/b5 = 1/(a+b)5.
iii)Prove that (1+cosA+sinA)/(1+cosA-sinA)=(1+sinA)/cosA.
iv)If tanx=k,find sinx/cos3x + cosx/sin3x.
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5 Answers
1Q2)
sin4xa + cos4xb = 1a+b
bsin4x + acos4x = aba+b
bsin4x + a(1 - sin2x)2 = aba+b
(a+b)2sin4x - 2a(a+b)sin2x + a2 = 0
this is quadratic in sin2x
we get sin2x = aa+b hence cos2x = ba+b
now substituting these values in sin12xa5 + cos12xb5
we get value as 1(a+b)5