Q37 of 186 Page 332

Prove that: (sin θ – 2 sin3 θ) = (2cos3 θ – cos θ) tan θ.

Consider R.H.S. = (2cos3 θ – cos θ) tan θ

= cos θ(2cos2 θ – 1)


= (2cos2 θ – 1)sin θ


Consider L.H.S. = (sin θ – 2 sin3 θ)


= sin θ(1 – 2 sin2 θ)


= sin θ[1 – 2(1 – cos2 θ)]


= sin θ [1 – 2 + 2cos2 θ]


= sin θ (2cos2 θ – 1)


Therefore, L.H.S. = R.H.S.


Hence, proved.


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Show that none of the following is an identity:

sin2 θ + sin θ = 2

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Show that none of the following is an identity:

tan2 θ + sin θ = cos2 θ

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If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that (m2+ n2) = (a2 + b2).

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(x2 – y2) = (a2 – b2)