(cot theta + 3)(3 cot theta + 1) = 3 cosec² theta + 10 cot theta
plyzzzz explain it with verification
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Answer:
Step-by-step explanation:
L.H.S. = ( cotθ + 3 ) ( 3 cotθ + 1 )
= cotθ ( 3 cotθ + 1 ) + 3 ( 3 cotθ + 1 )
= 3 cot²θ + cotθ + 9 cotθ + 3
= 3 ( cosec²θ - 1 ) + 10 cotθ + 3 ( ∵cot²θ = cosec²θ - 1 )
= 3 cosec² θ - 3 + 10 cotθ + 3
= 3 cosec² θ + 10 cotθ
= R.H.S.
∴L.H.S. = R.H.S.
Hence it is proved.
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