If a.cot theta =b then sin2 theta =?
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Answer:
acotθ+bcosecθ=p
bcotθ+acosecθ=q
⇒p
2
−q
2
=(p−q)(p+q)
=[acotθ+bcosecθ−bcotθ−acosecθ][acotθ+bcosecθ+bcotθ+acosecθ]
=[cotθ(a−b)−cosecθ(a−b)][cotθ(a+b)+cosecθ(a+b)]
=(a−b)(cotθ−cosecθ)(a−b)(cotθ−cosecθ)
=(a
2
−b
2
)(cot
2
θ−cosec
2
θ)
=(−1)(a
2
−b
2
)[∵cosec
2
θ−cot
2
θ=1]
=(b
2
−a
2
)
Hence, the answer is b
2
−a
2
.
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