Q21 of 104 Page 204

If tanθ + sin = a and tanθ — sinθ = b, then prove that a2 — b2 =

tan + sin = a [1]

tan — sin = b [2]


adding and subtracting [1] and [2]


2tanθ = a + b and 2sinθ = a–b


L.H.S


a2 — b2 = (a + b)(a–b)


⇒ a2 — b2 = (2tanθ)( 2sinθ)


⇒ a2 — b2 = 4tanθsinθ


R.H.S


4√(ab)


⇒


=







L.H.S. = R.H.S


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